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?