Question

A fair coin is flipped 15 times. What is the probability of getting exactly 7 heads?

Answer 1

no..it's not

Answer 2

each time the chance of getting heads is 1/2 so its 1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/32768

Answer 3

use the binomial distribution

Answer 4

\(\Large P(X=7)=_{15}C_7\cdot \left(\dfrac{1}{2}\right)^7\left(\dfrac{1}{2}\right)^{15-7}\)

Answer 5

@insanitycat, like I always tell students, use your "red flag" check. 1/32768 is a VERY miniscule probability, considering that you are talking about the probability of a coin flip coming up head on approximately half of the flips. That should send off a red flag in your head... "wait, something must not be right here..."

what you computed is the probability of any ONE particular combination of heads/tails in 15 flips.