Probability Question?

I assume you mean at least two.

What is the probability they all fall in different weeks? Call that Q.

Q = (51/52) x (50/52) x (49/52) x (48/52) x (47/52)

Probability at least two are in the same week is

P = 1 - Q

I am assuming you are asking what is the probability that there is at least 2 people who share a birthday.

If this is the case it is easier to compute the complement which is the probability that no one shares a birthday and then take 1 minus that value. This is computed by 52/52 * 51/52 * 50/52 * 49/52 * 48/52 * 47/52, since the first person can have his birthday any week and each subsequent person cannot have a birthday in each week someone earlier has their birthday. We then take 1 minus this value which equals about .25859

The question is not clear, do you mean "exactly two" will have the same birthday week, or "at least two" will have the same birthday week. I'll assume "at least two".

To do this, we find the prob. that none will share a birthday week, and then subtract from 1.

Prob. of no match is (52/52)x(51/52)x..(47/52)=.7414,

and then subtract from 1 to get .2586.

The probability of the week in which birthday lies is given by 1/52 means it can be any week of the year.

now the birthday of second person is also in the same week. so his probability is 1/7 as we have already decided the week.

therefore the total probability is (1/52)*(1/7).