Question

You flip a fair coin 7 times. What is the probability that the coin lands with the heads side up exactly 3 out of the 7 times?

Answer 1

35/128 ≈ 0.2374

Explanation:

The number of combinations of 7 things taken 3 at a time is ...

7·6·5/(3·2·1) = 7·5 = 35

The number of sequences in which the coins can land is 2^7 = 128.

Of those 128 sequences, 35 will have exactly 3 heads.

The probability is 35/128.