SOLUTION: Hi. I need help with this binomial probability problem. Suppose that an unfair coin comes up heads 56.9% of the time. The coin is flipped a total of 27 times. 1. What is the pro

Algebra ->  Probability-and-statistics -> SOLUTION: Hi. I need help with this binomial probability problem. Suppose that an unfair coin comes up heads 56.9% of the time. The coin is flipped a total of 27 times. 1. What is the pro      Log On


   

Question 982727: Hi. I need help with this binomial probability problem.
Suppose that an unfair coin comes up heads 56.9% of the time. The coin is flipped a total of 27 times.
1. What is the probability that you get at most 25 heads?

Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!

Given:
An unfair die with heads 56.9% of the time.
Find probability that up to 25 heads show up in 27 throws.

Solution:
Binomial probability distribution,
p=0.569
n=27
r=25
So,
P%28n%2Cr%29=C%28n%2Cr%29%2Ap%5Er%2A%281-p%29%5E%28n-r%29

P%2827%2C26%29=C%2827%2C26%29%2A0.569%5E26%2A%281-0.569%29%5E1=4.9976%2A10%5E-6
P%2827%2C27%29=C%2827%2C27%29%2A0.569%5E27%2A%281-0.569%29%5E0=2.444%2A10%5E-7

Therefore probability for getting up to 25 heads
P(27,0-25)=1-P(27,>25)=1-P(27,26)-P(27,27)
=1-4.9976%2A10%5E%28-6%29-2.444%2A10%5E%28-7%29=1-5.242%2A10%5E%28-6%29=0.9999948