Assignments in Mathematics Class IX (Term 2) PROBABILITY IMPORTANT TERMS, DEFINITIONS AND RESULTS P E = SUMMATIVE ASSESSMENT

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1 Assignments in Mathematics Cass IX (Term ) PROBABILITY IMPORTANT TERMS, DEFINITIONS AND RESULTS The science which measures the degree of uncertainty is caed probabiity. In the experimenta approach to probabiity, we find the probabiity of the occurrence of an event by actuay performing the experiment a number of times and record the happening of an event. The observations of an experiment are caed outcomes. A tria is an action which resuts in one or severa outcomes. An event of an experiment is the coection of some outcomes of the experiment. The emperica (or experimenta) probabiity P(E) of an event E is given by : ( ) P E = Number of trias in which E has happened Tota number of trias The probabiity of an event ies between 0 and (0 and incusive). A dice is a we baanced cube with its six faces marked with numbers to, one number on one face. Sometimes dots appear in pace of numbers. SUMMATIVE ASSESSMENT MULTIPLE CHOICE QUESTIONS. A coin is tossed 00 times with the foowing frequencies : Head :, Tai : Probabiities for each event are respectivey :,,,,. Two coins are tossed simutaneousy 00 times. The resuts are given beow : No heads : 0 times, one head : 0 times, two heads : 0 times. The probabiity of getting one head is :. In an experiment a coin is tossed 00 times. If the head turns up 0 times, the experimenta probabiity of getting a head is :. In a cricket match, a batsman hits a boundary times out of bas he pays. The probabiity that he hits a boundary is :. A survey of 0 men showed that ony of them know Engish. Out of them, if one is A. Important Questions seected at random, what is the probabiity that the seected man knows Engish? none of these. In a One-Day cricket match, a batsman payed 0 bas. The runs scored were as foows : Runs scored No. of bas 0 The probabiity that the batsman scored no run is : 0 0. A coin is tossed 00 times and head appears times. The probabiity of getting a tai is : 0 [ Mark]. A coin is tossed 00 times and head appeared 00 times. The sum of the probabiity of getting, DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

2 a head and the probabiity of getting a tai is :. Three coins are tossed simutaneousy 00 times with foowing outcomes : Outcomes heads heads head No head The probabiity of getting two heads is : 0. A survey of 00 men, showed that ony of them know Engish. Out of them one man is seected at random. The probabiity that the seected man does not know Engish is : packets of sat, each marked kg, actuay contained the foowing weights (in kg) of sat :.0,.000,.0,.0,.0,.00,.0,.00,.00,.0,.00,.0 Out of these packets, one packet is chosen at random. The probabiity that the chosen packet contains ess than kg of sat is :. In a survey of 00 students, 0 iked Mathematics and rest disiked it. The probabiity that a student chosen at random ikes Mathematics is : none of these. Foowing are the ages (in years) of 0 patients, getting medica treatment in a hospita : Age in years No. of patients One of the patients is seected at random. The probabiity that his age is 0 years or more but ess than 0 years is : 0. In an experiment, a coin is tossed 00 times. If the head turns up 0 times, then the probabiity of getting a tai is :. A dice is tossed 00 times simutaneousy, and the frequencies of various outcomes are given beow : Outcomes 0 0 The probabiity of getting is : Marks obtained by 0 students of a cass in a test of maximum marks 00 are given beow : Marks No. of students and above A student of the cass is seected at random. The probabiity that he gets ess than % marks is : An organisation seected 00 famiies and surveyed them to determine the number of girs in the famiy as foows. No. of girs in a famiy 0 No. of famiies The probabiity of a famiy having gir is : bubs are seected at random from a ot and their ife time (in hrs) is recorded in the form of a frequency tabe given beow :, DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

3 Life time (in hours) One bub is seected at random from the ot. The probabiity that its ife is 0 hours, is : 0 0. A dice is thrown 000 times and the outcomes were recorded as foows : Outcome If the dice is thrown once more, then the probabiity that it shows is : 0 0. In a medica examination of students of a cass, the foowing bood groups are recorded : Bood group A 0 AB B O A student is seected at random from the cass. The probabiity that he/she has bood group B, is : 0 0. A die is thrown times and the resuts were as foows : Outcomes 0 0 The probabiity of getting a prime number is :. Games payed by 00 students of a schoo are recorded as beow : Games No. of students Cricket Footba Tennis Badminton A student is chosen at random. The probabiity that he pays neither cricket nor footba is : 0 0. Three coins were tossed simutaneousy 00 times with the foowing frequencies of different outcomes : Outcomes Frequencies heads heads head No heads The probabiity of getting more than one head is : 0. 0 students of a cass were tested to find their puse rate. The foowing figures were obtained for the number of beats per minute : 0, 0,, 0,,,,,,,,,,,,,,,, 0 If a student is seected at random, the probabiity that his heart beat per minute is ess than 0 is :. Marks obtained by 0 students in a cass test of 00 marks are given beow : Marks No. of students The probabiity that a student obtains ess than 0% marks is :, DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

4 . A machine generated these 0 codes : {0A, AAA, ABC, B, B, BB, AC,,, }. A code is drawn at random to aot an empoyee. The probabiity that the code have at east two digits is : none of these. A dice is tossed 0 times and the resuts were as foows : Outcomes 0 0 The probabiity of getting either or is : 0. A coin is tossed 00 times with the foowing frequencies : Head :, Tai : The ratio of probabiities for each event is : : : : :. The weight of 0 students of a cass were recorded as beow: Weight (in kg) No. of students and above A student is chosen at random. The probabiity that his weight is 0 kg or more, is : 0. There are 000 Engineers, 000 Doctors and 00 Lawyers. If one professiona is chosen at random, the probabiity that he is an Engineer is :. The height of 0 students were recorded as beow: Height (in cm) No. of students A student is chosen at random. The probabiity that his height is ess than 0 cm is :. A coin is tossed 0 times and head appears times. If we toss the coin randomy, the probabiity of getting neither a head nor a tai is : 0. In a cricket match, a batsman hits a boundary times out of bas he pays. The probabiity that he did not hit a boundary is:. The saaries of 0 empoyees in an office are given beow : Saary (in Rs.) No. of empoyees or above An empoyee is seected at random. The probabiity that his saary is Rs 000 or more but ess than Rs 000 is : 0 0. The foowing tabe shows the bood groups of 0 students of a cass: Bood group A B O AB One student of the cass is chosen at random. What is the probabiity that the chosen student has either bood group A or B? 0 0. Three coins are thrown simutaneousy 0 times, with the foowing frequencies : Heads : 0 times, Heads : times, Head : times, No Head : times. P (getting heads) + P (getting no head) is equa to :, DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

5 In an experiment, a coin is tossed 00 times. If head turns up 0 times, the experimenta probabiity to get either a head or a tai is : 0. Number of matchsticks in matchboxes were recorded as beow :,, 0,,, 0,, 0,,,, 0,,,,,,,,,, 0,,,. If one matchbox is chosen at random, the probabiity that it contains exacty 0 matchsticks is :. A coin is tossed 00 times and head appears times. If we toss a coin at random, what is. A die is tossed 000 times and the outcomes are recorded in the foowing tabe. [T-II (0)] Outcome The probabiity of getting an even number is : 0 0. A coin is tossed times and the data is recorded as foows : [T-II (0)] Head : Tai : 0 The probabiity of not getting a head is : 0. Probabiity of not getting an even number when a die is thrown is : [T-II (0)]. A box has 0 bubs. Out of this are defective. A bub is chosen at random. Find the probabiity of the bub chosen, not being defective. [T-II (0)] 0. Which one cannot be the probabiity of an event? [T-II (0)] the probabiity of getting a tai? There are 0 students in a cass and out of them are girs. If a student is seected for ucky draw, the probabiity that a student must be a boy is : 0. Two coins are tossed 000 times and the outcomes are recorded as beow : Number of heads Based on this information, the probabiity for at most one head is : B. Questions From CBSE Examination Papers. Two coins are tossed simutaneousy for 00 times and the outcomes are as foows : [T-II (0)] Two heads : 00 One head : 0 No head : 0 The probabiity of getting one head is :. The probabiity of happening of an events is %. The probabiity of the event is : [T-II (0)] In an experiment, the sum of probabiities of a events is : [T-II (0)] 0.. If P (E) denotes the probabiity of an event E, then : [T-II (0)] P(E) < 0 P(E) > 0 P(E) P(E) 0. A bag contains x white, y red and z bue bas. A ba is drawn at the random, then the probabiity of drawing a bue ba is : [T-II (0)] z x+ y+ z x x+ y+ z 0 y x+ y+ z, DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

6 . In a survey, out of 00 students, it is observed that students ike mathematics. The probabiity that the students who do not ike mathematics is : [T-II (0)]. Out of students participating in a debate, 0 are girs. The probabiity that winner is a boy is : [T-II (0)]. In a cass, there are x girs and y boys. A student is seected at random, then the probabiity of seecting a boy is : [T-II (0)] x y x ( x+ y) y ( x+ y) y x. In a sampe survey of 0 peope, it was found that 00 peope have a secondary schoo certificate. If a person is seected at random, the probabiity that the person does not have such certificate is : [T-II (0)] A die is thrown once, a number is noted, then the probabiity that it is a prime number is : [T-II (0)] SHORT ANSWER TYPE QUESTIONS. Can the experimenta probabiity of an event be a negative number? If not, why?. Can the experimenta probabiity of an event be greater than? If not, why?. Can the experimenta probabiity of an event be zero? If not, why?. State whether the foowing is correct or not. The emperica probabiity P(E) of an event E happening is given by P(E) = Tota number of trias No.of trias in which the event happened. The probabiity of an event can be any number from 0 to. Is it true? Justify.. As the number of tosses increases, the ratio of the number of heads to the tota number of tosses wi be. Is it correct? if not, write the correct one.. In a cricket match, a batsman hits a sixer times out of bas payed. The probabiity that a sixer is not hit in a ba is : [T-II (0)] In a survey of chidren aged 0-0 months, it was found that iked to eat potato chips. If a chid is seected at random, the probabiity that he /she does not ike to eat potato chips is : [T-II (0)] In an experiment 00 drawing pins were dropped on a foor. anded point up and the rest anded point down. A pin is seected at random and dropped. What is the probabiity that the pin wi and point down? [T-II (0)] Sum of the probabiity of happening and not happening of an event is : [T-II (0)] 0 none of these 0. A fair coin is tossed 00 times and the head occurs times and tai times. The experimenta probabiity of getting a head is : [T-II (0)] A. Important Questions 0 0 [ Marks]. What is the probabiity of an impossibe event?. What is the probabiity of a sure event?. An unbiasd die is thrown. List a possibe outcomes. 0. Two coins are tossed simutaneousy. List a possibe outcomes.. Two coins are tossed 00 times and the outcomes are recorded as beow: No. of heads Based on this information, find the probabiity for (i) at most one head (ii) at east one head.. In a sampe study of 0 peope, it was found that 0 peope were government empoyees. If a person is seected at random, find the probabiity that the person is not a government empoyee., DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

7 . In a cricket match, a batsman hits a boundary times out of 0 bas payed. Find the probabiity that he did not hit a boundary. [T-II (0)]. Eeven bags of wheat four, each marked kg, actuay contained the foowing weights of four (in kg) :.,.0,.0,.00,.00,.0,.0,.,.0,.0,.00. Find the probabiity that any of these bags chosen at random contains more than kg of four. [T-II (0)]. A die is thrown 00 times, the frequency of outcomes,,,, and are noted in the foowing frequency distribution tabe : [T-II (0)] Outcome 0 0 Find the probabiity of occurrence of a prime number.. A dice is tossed 00 times and the outcomes are recorded as beow : [T-II (0)] Out come 0 Even number ess than Odd no. greater than 0 Find the probabiity of getting : The number Even number ess than. Foowing tabe shows the marks obtained by 0 students in a cass test : [T-II (0)] Marks obtained B. Questions From CBSE Examination Papers 0 0 Find the probabiity that a student secures 0 marks ess than 0 marks.. A survey of 00 students is done regarding the ikes and disikes about the subject mathematics. The data are given beow : [T-II (0)] Views Likes 0 Disikes 0 Find the probabiity that a student chosen randomy ikes mathematics does not ike mathematics. One card is drawn at random from a we shuffed deck of cards. Find the probabiity for getting a face card. [T-II (0)]. Two dice are thrown simutaneousy 00 times. Each time the sum of numbers appearing on their tops is noted and recorded as beow. [T-II (0)] Sum Find the probabiity of getting a sum : (i) more than 0? (ii) ess than or equa to? SHORT ANSWER TYPE QUESTIONS. The foowing tabe is an extract from a mortaity tabe. Age in years No. of persons surviving out of a sampe of one miion A. Important Questions [ Marks] (i) Based on this information, what is the probabiity of a person aged 0 of dying within a year? (ii) What is the probabiity that a person aged wi ive for years?. In a survey of 00 peope, it was found that read newspapers daiy and rest read newspapers occasionay. Find the probabiity that a person chosen at random : (i) reads newspaper daiy (ii) reads newspaper occasionay, DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

8 . The percentage of marks obtained by a student in monthy unit test are given beow : Unit test I II III IV V % of marks obtained 0 Find the probabiity that the student gets : (i) more than 0% marks (ii) ess than 0% marks (iii) more than 0% marks.. Bubs are packed in cartons, each containing 0 bubs. Seven hundered cartons were examined for defective bubs and the resuts are given in the foowing tabe : No. of defective bubs more than One cartoon was seected at random, what is the probabiity that it has : (i) no defective bubs? (ii) defective bubs from to? (iii) defective bubs ess than?. In a One Day Internationa, a batsman payed 0 bas. The runs score are as foows : Runs scored 0 No. of bas Find the probabiity that the batsman wi score : (i) runs. (ii) a four or a six run. (iii) 0 or or runs.. Over the past 00 working days, the number of defective parts produced by a machine is given beow: No. of defective parts Days Determine the probabiity that tomorrow s output wi have : (i) no defective part (ii) not more than defective parts (iii) more than defective parts? B. Questions From CBSE Examination Papers. The records of a weather station shows that out of the 0 consecutive days, its weather forecast were correct times. [T-II (0)] (i) What is the probabiity that on a given day it was correct? (ii) What is the probabiity that it was not correct on a given day?. Marks obtained by students of cass IX in Mathematics are given in the tabe : [T-II (0)] Marks (i) Find the probabiity that a student gets ess than 0% in a test. (ii) Find the probabiity that a student gets more than 0%.. A bag contains tickets which are numbered from to 00. Find the probabiity that a ticket number picked up at random [T-II (0)] (i) is a mutipe of (ii) is not a mutipe of.. Two coins are tossed simutaneousy. Find the probabiity of getting : [T-II (0)] (i) ateast one head (ii) both heads.. A die is thrown 000 times with the frequencies for the outcome,,,, and as given in the foowing tabe. [T-II (0)] Outcomes 0 0 Find the probabiity of getting a : (i) prime number as a outcome. (ii) number greater than as outcome.. 00 famiies with chidren were seected and foowing data is recorded. [T-II (0)], DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

9 No. of girs/famiy 0 N. of famiies Compute the probabiity of a famiy chosen at random having : (i) at east gir chid (ii) not more than gir chid. (iii) no gir chid.. A coin is tossed 00 times and head appeared 00 times. Find the sum of the probabiity of getting a head and the probabiity of getting a tai. [T-II (0)]. 00 cards marked from to 0 are paced in a box and mixed thoroughy. One card is drawn at random from the box. Find the probabiity that number on the card is [T-II (0)] (i) an even number (ii) a number which is a perfect square (iii) a prime number ess than 0. It is known that a box of 0 bubs contains defective bubs. One bub is taken out at random from the box. Find the probabiity of getting : (i) defective bub [T-II (0)] (ii) good bub. 0. A student opens his book and notes down the units digit on the right hand page of his book. He repeats the process for 0 times. The outcomes are recorded. [T-II (0)] Digits Based on the above information, find the probabiity of occurrence of : (i) or as unit s digit. (ii) At east as the unit s digit.. Fifty seeds were seected at random from each of bags of seeds and were kept under standardized conditions favourabe to germination. After 0 days, the number of seeds which had germinated in each coection were counted and recorded as foows : [T-II (0)] Bags No. of seeds germinated 0 What is the probabiity of germination of : (i) more than 0 seeds in a bag? (ii) seeds in a bag? (iii) more than seeds in a bag?. Two dice are thrown 00 times. Each time sum of two numbers appearing on their tops is noted as given in the foowing tabe. [T-II (0)] Sum What is the probabiity of getting a sum (i) (ii) more than 0 (iii) between and 0. Three coins are tossed simutaneousy 00 times with the foowing frequencies of different outcomes. [T-II (0)] Outcome heads heads head No head From the above, compute the probabiity of the foowing : (i) at east heads (ii) tais (iii) at most one head. A bag contains cards numbered from to. A card is drawn at random from the bag. Find the probabiity that the seected card bears number which is a mutipe of or. [T-II (0)]. The foowing tabe shows the performance of two sections of students in a mathematics test of 00 marks : [T-II (0)] Marks above Tota 0, DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

10 Find the probabiity that a student obtained : (i) ess than 0% in the mathematics test. (ii) marks 0 or above (iii) marks more than or equa to 0 but ess than 0.. The foowing frequency distribution tabe gives the weights of students of a cass. [T-II (0)] Weight in kg Tota Find the probabiity that the weight of a student is (i) more than or equa to kg (ii) ess than 0 kg (iii) more than or equa to 0 kg but ess than 0 kg. When three coins are tossed simutaneousy, find the probabiity of getting at east two tais. [T-II (0)]. Three coins are tossed simutaneousy 00 times with the foowing frequencies of different outcomes : [T-II (0)] Outcome Heads Heads Head No Head From the above data, find the probabiity of getting (i) heads, (ii) tais, (iii) tais.. A die is thrown 00 times. The frequency of outcomes of the events are given as under. [T-II (0)] Outcome 0 0 Find the probabiity of : (i) occurrence of an even number. (ii) occurrence of a number ess than. 0. The percentage of marks obtained by a student in monthy unit test are given beow : [T-II (0)] Unit Test I II III IV V % of marks 0 Find the probabiity that the student gets : more than 0% marks more than 0 % marks. Marks obtained by 00 students are shown in the foowing tabe : [T-II (0)] Cass Inverva Less than Tota 00 A student is seected at random. Find the probabiity that : he scores more than 0% marks. he scores ess than 0% marks.. A bag contains cards numbered from to 00. A card is drawn at random from the bag. Find the probabiity that the : [T-II (0)] card bears a number which is a mutipe of. card bears a number which is greater than or equa to 0.. Three coins are tossed simutaneousy 0 times with foowing frequency of different outcomes : [T-II (0)] Outcomes Heads 0 Heads 0 Head 0 No Head 0 Compute the probabiity of getting : (i) two heads (ii) at east two heads. In a survey of 00 famiies with chidren, seected randomy, the foowing data were recorded : [T-II (0)] Number of girs in a famiy 0 Number of famiies Cacuate the probabiity of a famiy, chosen at random has : (i) girs (ii) gir (iii) no gir. Two dice are thrown simutaneousy 00 times. Each time the sum of two numbers appearing on them is noted and recorded in the foowing tabe : [T-II (0)] Sum 0 0 0, DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us : 0

11 From the above data, what is the probabiity of getting a sum (i) more than 0? (ii) between and?. The foowing data shows the bood groups of 0 students of a cass. [T-II (0)] Bood group A AB B O No. of students 0 A student is seected at random from the cass. Find the probabiity that the student : (i) has bood group A (ii) has bood group O (iii) does not have bood group AB.. Foowing distribution gives the weight of students of a cass. [T-II (0)] Weight in kg. No. of students Find the probabiity that weight of a student in the cass is (i) at most 0 kg. (ii) at east kg. (iii) not more than 0 kg.. Three coins are tossed simutaneousy 000 times with the foowing frequencies of different outcomes : [T-II (0)] Outcome Heads 0 Head 0 No head 0 Find the probabiity of occurrence of each of these events.. The weeky pocket expenses of students are given in the foowing tabe : [T-II (0)] Pocket expenses (in Rs) 0 0 Find the probabiity that the weeky pocket money of a student is : Rs more than Rs ess than Rs 0. A bag contains bas out of which x are white. If one ba is taken out from the bag, find the probabiity of getting a white ba. If more white bas are added to the bag and the probabiity now for getting a white ba is doube the previous one, find the vaue of x. [T-II (0)]. The ages (in years) of workers of a factory are as foows : [T-II (0)] Age (in years) No. of workers and above If a worker is seected at random, find the probabiity that the worker is : (i) 0 years or more (ii) beow 0 years (iii) having age from 0- years., DEVENDRA NAGAR, SECTOR-, D/, RAIPUR, C.G, HELPLINE : -0, Visit Us :

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