# Homework Help: Probability question -- A test to see if a coin is fair...

1. May 29, 2015

### Mr Davis 97

1. The problem statement, all variables and given/known data

You want to see if a coin is fair. You flip it 5 times and count the number of heads. If H is the number of heads obtained in five flips of the coin, what is the P-value of the test when H equals 4?

2. Relevant equations
None

3. The attempt at a solution

To solve this problem, I thought that it would be correct to use the binomial PDF, to answer the question "If the probability of getting heads is .5, then what are the chances of getting 4 heads in 5 flips?" This gives .15625, which is not the right P-value. The correct answer is 3/16, but how do I get this value? What probability distribution to I use to obtain this P-value?

2. May 29, 2015

### Orodruin

Staff Emeritus
The p-value is not the probability of landing on the exact outcome. It is the probability of obtaining that or a more extreme outcome. I would also disagree on how the "correct" answer has chosen to define an outcome as extreme (getting 1 head is as extreme as getting 4, getting 0 is as extreme as getting 5 - you would typically not design a test which broke the symmetry).

3. May 29, 2015

### Ray Vickson

For binomial(5, 1/2), they take p-value = P(4) + P(5) = (5/32) + (1/32) = 3/16, so they take p-value = P(4 or more heads).