If you flip a fair coin 5 times, what is the probability that you will get exactly 3 tails?

Solution:

Given a fair coin is flipped 5 times

Total sample space while tossing a coin 5 times is 2⁵ = 32

Let P be the probability of getting exactly 3 tails

We can calculate by using binomial expansion

⁵C₃ = 5!/(3!2!)

= 10 ways to get exactly 3 tails.

P(exactly 3 tails) = 10/32

= 5/16

The probability of getting exactly 3 tails is 5/16.

If you flip a fair coin 5 times, what is the probability that you will get exactly 3 tails?

Summary:

If you flip a fair coin 5 times, the probability that you will get exactly 3 tails is 5/16.