# What is the probability of Jack finding Sam at the last bar?

Jack and Sam are friends. It is Saturday and Sam forgot his phone home. Jack knows that there is a 2/3 probability that Sam goes to a party. There are 10 clubs in town and all have an equal probability of Sam being in one of them. Jack has checked on 9 bars. What is the probability of Jack finding Sam at the last bar? I've come up with this result:

P(Sam going to party)=P(A) = 2/3 = 0.667

P(Sam being one of the 10 bars) = P(B) = 1/5=0.2

Jack has visited 9 bars.

P(Sam being at the last bar) = 1/2 * 2/3 = 2/6 = 1/3 = 0.33

Is this the correct way to solve this problem?

• If this is a homework problem, you might consider adding the "self-study" tag. Also, to clarify: does Sam going to a party mean he goes to one of these clubs, or does it mean he goes to a party instead of going to a club? In any case, consider that at this point, if he's gone clubbing he cannot be in another club because those have been checked already. If he's gone clubbing, he'll be in this one, and if he isn't in this one, he hasn't gone clubbing. Try to work it out from there. – Ruben van Bergen Oct 11 '17 at 11:38