The adventures of Josh and Dan: GMAT Probability

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The adventures of Josh and Dan: GMAT Probability

QOD Probability GMAT

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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.