A class has 40 students aged 17 to 34 What is the probabilty

A class has 40 students aged 17 to 34. What is the probabilty that at least two students are the same age? Why?

Solution

Here we have that P(atleast two same ages )= 1- P(no same age)

Now total favorable cases for no same age are 34-17= 18 ( as all will be of different ages)

Thus Probability ( different ages ) = Total favorable case/total case =18/40

And accordingly Probability (atleast two same ages ) =1-18/40 = 22/40 = 11/20

So last required answer is 11/20.