A single man is searching to find his future wife through a

A single man is searching to find his future wife through a dating website. His search ends when he finds his perfect match. The ladies he meets are independent of each other and he has a 20% chance of finding his perfect match when dating a lady. What is the probability that his search takes more than 2 but less than 6 dates?

Solution

Probability of finding perfect match when dating with each lady is 20% = 1/5 = 0.2

Total no. of ladies that the person has dated = lessthan 6 = 5

The prob. of occuring either events = P(A or B or C) = P(A) + P(B) + P(C) - P(A and B and C)

But, the events are individual, so the P(A and B and C) = 0.

The probability of his search takes more than 2 and less than 6 = P(3rd lady) + P(4th lady) + P(5th lady)

= 1/5 + 1/5 + 1/5 = 0.6.