If you flip a fair coin 7 times, what is the probability that you will get exactly 4 tails?

Answer 1

With a fair coin, with P(tail) = 1/2, we use the binomial distribution.

P(4) = C(7,4)(1/2)^4(1/2)^(7-4) = C(7,4)(1/2)^7 = C(7.4)/2^7 = 35/128 = 0.2734375

Alternatively, you can use a calculator to get this probability with 7 trials, 4 successes, and probability = 1/2

For example, in Excel, =binom.dist(4,7,1/2,0) yields this result.