A fair coin is tossed 5 times. What is the probability of exactly 3 heads?

Solution:

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having n number of outcomes, the number of favorable outcomes can be denoted by x.

The formula to calculate the probability of an event is as follows.

Probability(Event) = Favourable Outcomes/Total Outcomes = x/n

Considering a fair coin, after 5 flips, there are 2⁵ = 32 different arrangements of heads and tails.

To get exactly 3 heads,

⁵C₃ = 5!/ 3!2! = 10 ways

P(exactly 3 heads) = 10/32 = 5/16

Therefore, the probability of exactly 3 heads is 5/16.

A fair coin is tossed 5 times. What is the probability of exactly 3 heads?

Summary:

A fair coin is tossed 5 times. The probability of exactly 3 heads is 5/16.