Compute approximately the probability that you need to toss

Compute approximately the probability that you need to toss a fair coin more than 120 times in order to observe 40 Tails.

Solution

Let X be the no of tails

X is binomial with (120,0.5)

P(x=40) = 120C40 (0.5)¹²⁰

⁼8.618x10^-5

Hence prob for tossing more than 120 times = 1-8.618x10^-5

= 0.999914