Use the first two Bonferroni inequalities to compute an uppe

Use the first two Bonferroni inequalities to compute an upper and a lower bound on the probability that in a group of 60people, at least 3 were born on the same day.

Solution

There are 60 people.Atleast 3 were born on the same day.

For one person to be borne on a particular day = =0.00274

As this is an independent event for 3 persons =

Probability (X>=3) = Binomial prob with independent outcomes with n =60

= 0.000626

This can be written as

P(X>=3) = 1-P(X<3) = 1-0.9994 = 0.0006

Thus we can calculate in two ways for problems like this.