n( black) n( joker) n( red joker) Solutions to Unit 1.3 1a) { 7 of diamonds} 1b) { ace of spades, ace of diamonds, ace of hearts, ace of clubs}

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Cornelia Burke
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1 Solutios to Uit. a) { 7 of diamods} b) { ace of spades, ace of diamods, ace of hearts, ace of clubs} c) {,,, 5, 6, 7,, 9,0}all of clubs d) {,, 6,,0} of clubs, diamods, hearts, ad spades a) There are 5 possible outcomes b) P ( black) c) P ( red) 5 5 ( black) ( all possible) ( red) ( all possible) d) There are o possible outcomes therefore the probability is 0 a) P ( joker) ( joker) ( all possible cards) 5 7 b) P ( red joker) ( red joker) ( all possible cards) 5

2 c) P ( quee) d) P ( black) e) P ( <0) f) P ( red) 5a) P ( tail) 5b) P ( ) ( quee) ( all possible cards) 5 7 ( black) ( all possible cards) 7 5 ( <0) ( all possible cards) 6 5 ( red) ( all possible cards) 5 6 ( tail) ( all possible cards) ( ) ( all possible cards)

3 5c) P ( red) 5d) P ( B7) ( red) ( all possible cards) 6 5 5e) P ( <jack) ( B7) ( all possible cards) 5 7 ( <jack) ( all possible cards) 0 5 0

4 Uit. Solutios 6. a) P( A ) A S b) P( A ) c) P( A ) 7. a) P( A) ( odd umber) ( ay umber) A S ( divisible by ) ( ay umber) ( <) ( ay umber) A S A S ( red blocks) ( umber blocks)

5 b) P( A) ( A) ( red blocks) ( umber blocks). a) P( A) b) P( A ) c) P( A ) ( S's) ( letters) A S A S A S ( M's) ( letters) ( vowels) ( letters)

6 0 Possible values {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} ( A) 0. a) P( A) S 0 b) P( A) 0 c) P( A). ( all heads) ( possible values) 7 ( tail, tail, tail) ( possible values) A S ( HHT, HTH, THH) ( possible values) A S a) ( S ) 6 Die 5 6,,,, 5, 6,,,,, 5, 6,,,,, 5, 6,,,,, 5, 6, 5, 5, 5, 5, 5 5, 5 6, 5 6, 6, 6, 6, 6 5, 6 6, 6

7 b) P( A) A S ( totals 7) ( possible values) c) ( ) P( A) ( A) ( totals 7) ( possible values) % this will be equal to the probability ratio we eed 00 let the umber of caffeie-free diets be x, ( diet) 00 all driks 6 + x 00 + x 96 + x x 6 56x x 6

8 Uit. Solutios. a) {6, 9} b) {5,, 6, 9,, 0} c) {9,0} d) {,, 9, 0, 6, } e) f) {9} 6. a) S C T 0 7 b) P( C ) C S 0 0 c) P( C ) T 0

9 d) P( ) P( ) ( ) S HA C 6 The umber combied i both sets is 50- Let HA represet Head aches oly, B represet both, ad C represet colds Therefore HA+B0 C+B HA+B+C We have three equatios ad three variables, therefore we ca do this. Rewrite the first two equatios i terms of B HA0-B C-B Plug these ito the third equatio. (0-B)+B+(-B) 5-B B6 Therefore HA 0 6 C 6

10 b i) studets have just a headache P HA HA S b ii) ++6 have headache or cold ( or C) P HA ( or C) HA b iii) +6 have o cold symptom P ( oe) ( oe)

11 Uit.6 Solutios a) P( A B) P( A) + P( B) P( A B) P( A B) P( A B) P( A B) 0 Sice P( A B) 0, mutually exclusive. b) P( A B) P( A) + P( B) P( A B) Sice P( A B) 0.5, ot mutually exclusive c) P( A B) P( A) + P( B) P( A B) P( B) P( B) P( B) 0.6 Sice P( A B) 0, mutually exclusive ( a) remember ad B B Sice mutually exclusive P( A B) 0 ) b) P( A B) P( A) + P( B) P( A B) c Sice all probabilities must add up to, ad A ad B are mutually exclusive P(A)+P(B)+P(C) P P(C)0.5

12 5. Let A represet the evet that it is a female Let B represet the evet that it is a tetra ( female or tetra) ( ) P( A) + P( B) P( A B) ( A) ( B) ( A B) + P B Let A represet the evet of drawig a ace Let B represet the evet of drawig a club ( ) + ( ) ( A) ( B) ( A B) + B P B B a) Let A represet the evet of beig taller tha 5 cm Let B represet the evet of havig dark hair ( B) P( A) + P( B) P( A B) ( ) + P( A B) P B A B ( B) ( B)

13 b) Let A represet the evet of beig taller tha 5 cm Let B represet the evet of havig dark hair rom above P( A B) c) Let A represet the evet of beig taller tha 5 cm ( ) P( A) Uit.7 Solutios a) Let A represet the evet that the studet is male. Let B represet the evet that the studet likes school P B A ( B) P( A) A S 9 A ( B) ( B) P( B A ) 9 9

14 The probability of the evet that a studet likes school give that the studet is male is. 9 b) Let A represet the evet that the studet dislikes school. Let B represet the evet that the studet is female. P B A ( B) P( A) ( A) A ( B) P B A ( B) The probability of the evet that a studet is female give that the studet dislikes school is. 5a) Let A represet the evet that the patiet is a smoker. Let B represet the evet that the patiet is dyig from lug cacer. P B A ( B) P( A)

15 A S A ( B) ( B) P( B A ) The probability of the evet that a patiet will die from lug cacer give that the 6 patiet is a smoker is 50. 5b) Let A represet the evet that the patiet is a o-smoker. Let B represet the evet that the patiet is dyig from lug cacer. P B A ( B) P( A) A S A ( B) ( B)

16 0 P( B A ) The probability of the evet that a patiet will die from lug cacer give that the patiet is a o-smoker is 750.

17 6. Let A represet the evet that first marble is red. Let B represet the evet that the secod marble is red. P( A B) P( A B) P( A) A S P B A B A 7 P( A B) 7 9a) Let A represet the evet that first draw is a joker. Let B represet the evet that the secod draw is a ace. P( A B) P( A B) P( A) P B A ( A) 5 B A 5 P( A B) 5 5

18 9b) Let A represet the evet that first draw is a umbered card. Let B represet the evet that the secod draw is a red joker. P( A B) P( A B) P( A) A S P B A 6 5 B A 5 6 P( A B) b) Let A represet the evet that first draw is a quee. Let B represet the evet that the secod draw is a quee. P( A B) P( A B) P( A) P B A ( A) 5 B A 5 P( A B)

19 9d) Let A represet the evet that first draw is a black card. Let B represet the evet that the secod draw is a black card. P( A B) P( A B) P( A) A S P B A 7 5 B A P( A B) e) Let A represet the evet that first draw is a umbered card below 0. Let B represet the evet that the secod draw is the same umbered card. P( A B) P( A B) P( A) A S P B A 5 B A 5 P( A B)

20 9f) Let A represet the evet that first draw is a red joker or red ace. Let B represet the evet that the secod draw is a red joker or ace. It is easier to fid complemetary because of the either draw aspect. ( B ) a) Let A represet the evet that first draw is a red marble. Let B represet the evet that the secod draw is gree marble. B ( B) P( A) A S P( A B) P( A B )

21 9b) Let A represet the evet that the first marble is red Let B represet the evet that the secod marble is red. P( A B) P( A B) P( A) P B A A S 6 0 B A P( A B) 9 0 9c) Let A represet the evet that the first marble is gree. Let B represet the evet that the secod marble is gree. P( A B) P( A B) P( A) P B A A S 0 B A 9 P( A B) 9 0 5

22 9b) Let A represet the evet that the first marble is red Let B represet the evet that the secod marble is red. We have two situatios ( red red) + ( gree red) ( red red) ( red) + ( red gree) ( gree) P P P P P P Uit. Solutios a) T T T T T T T T T T T T T T T

23 P b) ( perfect ) 6 ( perfect ) or

24 c) correct icorrect P correct or 6 we ca look at it this way, we multiply by because there are ways of havig correct. a) (7D7D) b) (AS7D) c) (CC, CC, CC 0C9C, 0C0C) d) (ASC, ASC, AS6C, AD0C) a) 6x66 b) The oly way to obtai a sum of is white ad red c) R W W R

25 Uit.9 Solutios 5a) ( cards) ( dice) There are 0 possible outcomes 5b) The elemets of the sample space (card umber ad suit, umber o dice) 5ci) Let A represet the evet of drawig a eve card Let B represet the evet of a eve umber o die P ( eve ad eve) P( A B) P( A) P( B) ( A) ( B) ( S ) ( S ) cii) Let A represet the evet of drawig a eve card Let B represet the evet of a odd umber o die P ( eve ad odd) P( A B ) P( A) P( B) ( A) ( B) ( S ) ( S ) 0 0 6

26 5ciii) Let A represet the evet of drawig a card Let B represet the evet of a umber less tha or equal to umber o die P ( ad ) P( A B ) P( A) P( B) ( A) ( B) ( S ) ( S ) civ) Let A represet the evet of drawig a suit of card Let B represet the evet of umber o die Arragemets are {(,6); (,6); (,); (,); (5,); (6,)} ( sum7) ( ) P( A) P( B) ( A) ( S ) ( B) ( S ) P B arragemets 5civ) Let A represet the evet of drawig a suit of card Let B represet the evet of umber o die Arragemets are {(5,6); (6,5); (7,); (,); (9,); (0,)} ( sum7) ( ) P( A) P( B) ( A) ( S ) ( B) ( S ) P B arragemets

27 6a) Let A represet the evet of drawig a joker first Let B represet the evet of drawig a ace o the secod ( ) B P B This is ot coditioal because we do ot require the fidig of the probability of drawig a ace give that the joker was draw. 6b) Let A represet the evet of drawig a umbered card first Let B represet the evet of drawig a red joker o the secod ( ) B P B c) Let A represet the evet of drawig a quee card first Let B represet the evet of drawig a quee o the secod ( ) B P B d) Let A represet the evet of drawig a black card first Let B represet the evet of drawig a black o the secod ( ) B P B

28 6e) Let A represet the evet of drawig a umbered card < 0 first Let B represet the evet of drawig the same o the secod ( ) B P B f) Let A represet the evet of drawig a red joker or red ace card first Let B represet the evet of drawig a red joker or red ace o the secod Easier to do complemet. ( ) ( ) ( ) B P B a) S 000 b) P ( edig with a 5) c) P ( first is or ) ( last is 5) ( or )

29 Uit.0 Solutios a) Let A represet the evet of beig a uio member A S 5 0 b) Let A represet the evet of beig a uio member Let B represet the evet of beig a uio member Notice the ame is ot replaced ( ) ( A) ( B) ( S ) ( S ) B P B c) Let A represet the evet of beig a uio member Let B represet the evet of beig a uio member Let C represet the evet of beig a uio member Let C represet the evet of beig a uio member Notice the ame is ot replaced ( ) ( A) ( B) ( C) ( D) ( S ) ( S ) ( S ) ( S ) B C D P B P C P D

30 d) We have possible situatios NUUU, UNUU, UUNU, UUUN We wat P ( NUUU UNUU UUNU UUUN ) P ( NUUU ) + P( UNUU ) + P ( UUNU ) + P ( UUUN ) a) Let A represet the evet of drawig a chocolate bar first Let B represet the evet of drawig a chocolate bar secod ( ) B P B b) Let A represet the evet of drawig a chocolate bar first Let B represet the evet of drawig a chocolate bar secod Let C represet the evet of drawig a fruit bar first Let D represet the evet of drawig a fruit bar secod Let E represet the evet of drawig a toffee bar first Let represet the evet of drawig a toffee bar secod ( ) + ( ) + ( ) P( A) P( B) P( C) P( D) P( E) P( ) B P C D P E keep ay cady c) P

31 0a) P( spedig $000) P( st moth) P( d moth) P( rd moth) 0b) The two situatios are spedig $5000 or $6000 P ( 6000) P ( 5000) we sped 000, 000, 000 we eed to multiply by because of three cases three cases (000, 000, 000); (000, 000, 000); (000, 000, 000) we ca look at it this way ( 000, 000, 000) ( 000,000, 000) ( 000, 000,000) P P P ( more) ( 5000) + ( 6000) P P P + spedig $ c) P

Mathematics. ( : Focus on free Education) (Chapter 16) (Probability) (Class XI) Exercise 16.2

Mathematics. ( : Focus on free Education) (Chapter 16) (Probability) (Class XI) Exercise 16.2 ( : Focus on free Education) Exercise 16.2 Question 1: A die is rolled. Let E be the event die shows 4 and F be the event die shows even number. Are E and F mutually exclusive? Answer 1: When a die is