Quant Question Of The Day: 160
Counting and Probability
Four standard six-sided dice are rolled. Find the probability that, for each pair of dice, the product of the two numbers rolled on those dice is a multiple of 4.
1. 1/108
2. 31/432
3. 1/16
4. 13/69
If any two of the dice show an odd number, then this is impossible, so at most one of the dice can show an odd number. We take two cases: Case 1: If exactly one of the dice shows an odd number, then all three other dice must show a multiple of 4; which can only be the number 4: The probability that this occurs is 4 × ½ × (1/6)3 = 1/108 Case 2: If all of the dice show even numbers, then the condition is satisfied. The probability that this occurs is (1/2)4 = 1/16 The total probability is: 1/108 + 1/16 = 31/432
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