Anyone else think that Josh and Dan have too much time on their hands? Click here for the answer and explanation.

Since Josh must have more than 12 apples, it mean that he must win at least 4 times out of 6 times; also he must have less than 18 apples, it means he must not win all 6 times. So he should win 4 or 5 times.

Since he can win 4 or 5 times in any order, the number of ways he can win = 6C4 + 6C5 = 6C2 + 6C1 = (6.5/1.2) + 6 = 15 + 6 = 21 ways; nCr = nCn – r

The probability of winning 4 times and losing 2 times in a particular trial = (1/2)4 = 1/64. The probability of getting Heads = probability of getting Tails = 1/2. Similarly, the probability of winning 5 times and losing once in a particular trial = (1/2)5*1/2 = (1/2)6 =1/64.

Since the probability of winning 4 times or 5 times in a particular trial are equal, the probability of winning 4 times or 5 times = 21(1/64) =21/64

**Correct choice is B.**