# Math Help - Finding probabilities of two events.

1. ## Finding probabilities of two events.

Suppose 9 balls are distributed amongst 12 urns in such a way that no more than one ball is put in any one urn, and that all such arrangements are equally likely.

(i) What is the probability that a specified urn will contain a ball?

(ii) If the urns are placed in a row before the balls are distributed, what is the probability that at least two of the first four urns will be empty?

Thanks for any help.

2. Sure this is a university level question?

(i)
You know 9 urns have a ball in, and there are 12 urns total. the probability you want is 9/12

(ii)
Work out

P(at least 2 empty) = 1 - P(0 empty) - P(1 empty)

P(0 empty)= $\frac{9}{12} * \frac{8}{11} * \frac{7}{10}* \frac{6}{9}$

P(1 empty) = $\frac{9*8*7*3}{12*11*10*9} \times 4$