Twenty water balloons are presented for inspection four are

Twenty water balloons are presented for inspection; four are suspected to have leaks. If two of these water balloons are selected at random without replacement, what is the probability that one balloon of the two selected will have a hole in it?

Solution

4 out of 20 balloons have leaks, that is, the probability selecting a defective baloon is 4/20 = 0.2. Now, if two of te water baloons are selected without replacement, then the probability that one balloon of the two selected will have a hole/defective is probability of selecting defective on first draw and non-defective on second draw or selective nondefective on first draw and defective on second draw. The first methods is possible with probability (1/4)(1/16) while the second method is possible with probability (1/16)(1/4), and hence the overall probability is twice of (1/4)(1/16), that is, 1/32.