Question

2. In a group of 5 teenagers, what is the probability that at least two of them were born in the same year?

Answer 1

A teenager can have the age from 13 to 19, both inclusive, which are a total of 7 years. As each of the 5 teenagers can independently have any of these ages, the total number of possibilities S in terms of the year of birth are

The event E that at least two of them were born in the same year, shall be too complicated to evaluate. Its complement, that no two are born in the same year, in much simpler to calculate. We need to select 5 different years out of 7 possibilities, and then distribute them amongst the 5 teenagers. So this is a case of permutation, and the required no of ways are

Hence, the complement probability is

The desired probability is

The probability that at least two teenagers are born in the same year is about 85%