binomial probability distributions
DESCRIPTION
Lesson 10.1. Binomial Probability Distributions. 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) = n C k ∙ p k q n-k. Example 1. - PowerPoint PPT PresentationTRANSCRIPT
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
5 - 10