binomial probability distributions

Lesson 10.1

Formula on p. 541

Suppose that in a binomial experiment with n trials the probability of success is p in each trial, and the probability of failure is q, where q = 1 – p. Then,

P(exactly k successes) = nCk∙ pkqn-k

Example 1

The probability of getting a sum of 7 in a toss of two fair dice is known to be 1/6.

What is the probability of getting exactly 2 7s in 5 tosses.

5C2 (1/6)∙ 2(5/6)3

.16

Example 2 Suppose a baseball player has a .300 batting

average. A. If, in fact, the player has a .300 probability

of getting a hit each time at bat, determine the probability distribution for the number of hits in 5 at-bats in a game.

0 .168

1 .36

2 .308

3 .132

4 .028

5 .002

Example 2 (continued)

How unusual is it for this batter to get 3 or more hits in a game with 5 at-bats?

.132 + .028 + .002 = 16%

Not particularly unusual!

0 .168

1 .36

2 .308

3 .132

4 .028

5 .002

Example 3 A coin that is biased so that heads occurs

60% of the time is tossed 50 times by someone who does not know it is biased. What is the probability that between 23 and 27 heads occurs, so that the person is, by mistake, rather sure the coin is fair?

50C23 (.60)∙ 23(.4)27

23 1.5%

24 2.59%

25 4%

26 5.84%

27 7.78%

21.71%; need more tosses!

Example 4

Draw graphs of the binomial probability distributions when p = .6 when n = 10

Binomial probabilities on your calculator 2nd vars

0 which is : binompdf(n, p, x)

Where n = number of trials

P = probability of success

X = number of successes

To do a binomial distribution at once…

2nd vars 0 Binompdf (n, p) If you would like to graph this or

calculate other information, store it into a list

Ans sto L2

n = 10, p = .60 .000105

1 ,99157

2 .01062

3 ,04247

4 .11148

5 .20066

6 .25082

7 .21499

8 .12093

9 .04031

10 .00605

Homework

Pages 631 – 632

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