All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(a)

(i)

Alternatively,

(ii)

When , required probability

(b)

Key GC with either sequence or use table functions.

We want to solve

Plot and check for the x that gives a corresponding value that is less than

(c)

When , probability that all 21 people have different birthdays

Probability that all 21 people have different birthdays

Thus, when , probability that at least two of the people are the same birthday (more than )

### KS Comments:

A very interesting probability question here. This show show counter intuitive probability is! The results shows that the we can expect to find someone with the same birthday in a room of 23, more than half the time.