Objective - To understand experimental probability

Objective - To understand experimental probability

Probability THEORETICAL EXPERIMENTAL Theoretical probability can be found without doing and experiment. Experimental probability is found by repeating an experiment and observing the outcomes.

Probability Theoretical # of favorable outcomes # of possible outcomes Experimental # of successess # of trials P ( boy ) = boy boy or girl P ( boy ) = actual #of boys born actual # of babies P ( boy ) = 1 2 - Based on equally likely outcomes P ( boy ) = 1.691,384 3,288,536 P( boy )» 0.514» 51.4% - Based on actual past events.

How can you tell which is experimental and which is theoretical probability? Experimental: You tossed a coin 10 times and recorded a head 3 times, a tail 7 times P(head)= 3/10 P(tail) = 7/10 Theoretical: Toss a coin and getting a head or a tail is 1/2. P(head) = 1/2 P(tail) = 1/2

THEORETICAL PROBABILITY I have a quarter My quarter has a heads side and a tails side Since my quarter has only 2 sides, there are only 2 possible outcomes when I flip it. It will either land on heads, or tails HEADS TAILS

THEORETICAL PROBABILITY When I flip my coin, the probability that my coin will land on heads is 1 in 2 What is the probability that my coin will land on tails?? HEADS TAILS

Theoretical Probability Right!!! There is a 1 in 2 probability that my coin will land on tails!!! A probability of 1 in 2 can be written in three ways: As a fraction: ½ HEADS As a decimal:.50 As a percent: 50% TAILS

Theoretical probability When I spin this spinner, I have a 1 in 4 chance of landing on the section with the red A in it. A A A A

Theoretical Probability A 1 in 4 chance can be written 3 ways: As a fraction: ¼ As a decimal:.25 As a percent: 25% A A A A

Theoretical Probability I have three marbles in a bag. 1 marble is red 1 marble is blue 1 marble is green I am going to take 1 marble from the bag. What is the probability that I will pick out a red marble?

Theoretical Probability Since there are three marbles and only one is red, I have a 1 in 3 chance of picking out a red marble. I can write this in three ways: As a fraction: 1/3 As a decimal:.33 As a percent: 33%

Experimental Probability Experimental probability is found by repeating an experiment and observing the outcomes.

Experimental Probability Remember the bag of marbles? The bag has only 1 red, 1 green, and 1 blue marble in it. There are a total of 3 marbles in the bag. Theoretical Probability says there is a 1 in 3 chance of selecting a red, a green or a blue marble.

Marble number red blue green 1 1 2 3 4 5 6 Experimental Probability Draw 1 marble from the bag. It is a red marble. Record the outcome on the tally sheet

Experimental Probability Put the red marble back in the bag and draw again. This time your drew a green marble. Record this outcome on the tally sheet. Marble number red blue green 1 1 2 1 3 4

Experimental Probability Place the green marble back in the bag. Continue drawing marbles and recording outcomes until you have drawn 6 times. (remember to place each marble back in the bag before drawing again.)

Experimental Probability After 6 draws your chart will look similar to this. Look at the red column. Of our 6 draws, we selected a red marble 2 times. Marble number red blue green 1 1 2 1 3 1 4 1 5 1 6 1 Total 2 1 3

Experimental Probability The experimental probability of drawing a red marble was 2 in 6. This can be expressed as a fraction: 2/6 or 1/3 a decimal :.33 or a percentage: 33% Marble number red blue green 1 1 2 1 3 1 4 1 5 1 6 1 Total 2 1 3

Experimental Probability Notice the Experimental Probability of drawing a red, blue or green marble. Marble number red blue green 1 1 2 1 3 1 4 1 5 1 6 1 Total 2 1 3 Exp. Prob. 2/6 or 1/3 3/6 or 1/6 1/2

Comparing Experimental and Theoretical Probability Look at the chart at the right. Is the experimental probability always the same as the theoretical probability? red blue green Exp. Prob. 1/3 1/6 1/2 Theo. Prob. 1/3 1/3 1/3

Comparing Experimental and Theoretical Probability In this experiment, the experimental and theoretical probabilities of selecting a red marble are equal. red blue green Exp. Prob. 1/3 1/6 1/2 Theo. Prob. 1/3 1/3 1/3

Comparing Experimental and Theoretical Probability The experimental probability of selecting a blue marble is less than the theoretical probability. The experimental probability of selecting a green marble is greater than the theoretical probability. red blue green Exp. Prob. 1/3 1/6 1/2 Theo. Prob. 1/3 1/3 1/3

Experimental probability Experimental probability is found by repeating an experiment and observing the outcomes. P(head)= 3/10 A head shows up 3 times out of 10 trials, P(tail) = 7/10 A tail shows up 7 times out of 10 trials

Event - Spinning the spinner Outcome - A possible result Probability = # of favorable outcomes # of possible outcomes Find the probability of each event. 1 5 1. P(7)= 3. P(# <6)= 8 8 4 2. P(even #)= 4. P(#>4)= 8 = 1 1 2 2

Compare experimental and theoretical probability Both probabilities are ratios that compare the number of favorable outcomes to the total number of possible outcomes P(head)= 3/10 P(tail) = 7/10 P(head) = 1/2 P(tail) = 1/2

QUADRILATERALS Theoretical Probability Experimental Probability

QUADRILATERALS Theoretical Probability what is expected to happen Experimental Probability result of an experiment probability are ratios that compare the number of favorable outcomes to the total number of possible outcomes

Identifying the Type of Probability A bag contains three red marbles and three blue marbles. P(red) = 3/6 =1/2 Theoretical (The result is based on the possible outcomes)

Identifying the Type of Probability Trial Red Blue 1 1 2 1 3 1 4 1 5 1 6 1 Total 2 4 You draw a marble out of the bag, record the color, and replace the marble. After 6 draws, you record 2 red marbles P(red)= 2/6 = 1/3 Experimental (The result is found by repeating an experiment.) Exp. Prob. 1/3 2/3