A probability problem by Mehdi Hakim-Hashemi
Probability
Level
3
A pair of dice is rolled until a sum of either 5 or 7 appears. What is the probability that a 5 occurs first?
The answer is 0.4.
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1 solution
Our required sample space includes those ordered-pairs that sum to either 5 or 7, namely:
( 1 , 4 ) ; ( 4 , 1 ) ; ( 2 , 3 ) ; ( 3 , 2 ) ; ( 1 , 6 ) ; ( 6 , 1 ) ; ( 2 , 5 ) ; ( 5 , 2 ) ; ( 3 , 4 ) ; ( 4 , 3 )
We have 4 such pairs that sum to 5 over a sample space of 10 total pairs. Hence, the probability of summing to 5 first equals 1 0 4 = 0 . 4 .