If you flip a fair coin 7 times, what is the probability that you will get exactly 2 tails?

Solution:

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

Probability(Event) = Favourable Outcomes/Total Outcomes

We know that coin has two faces: head and tail.

The total number of outcomes is 2⁷.

As per the conditions given in the question,

There are 7 × 6 = 42 ways of having two tails in 7 flips.

The two tails can be taken in any order. Thus we conclude there are 42/2 = 21 ways of having two tails in 7 flips.

Then, the probability that you will get exactly 2 tails = (21/2⁷)= 21/128

Therefore, the probability that you will get exactly 2 tails is 21/128.

If you flip a fair coin 7 times, what is the probability that you will get exactly 2 tails?

Summary:

If you flip a fair coin 7 times, the probability that you will get exactly 2 tails is 21/128.