A probability problem by A Former Brilliant Member

Probability Level 2

Bob rolls a standard 6 6 -sided die once. Alice rolls a second standard 6 6 -sided die once. Bob wins if the values shown have a positive difference of exactly 1 1 . What is the probability that Bob wins?

5 18 \dfrac{5}{18} 1 36 \dfrac{1}{36} 10 18 \dfrac{10}{18} 5 36 \dfrac{5}{36}

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The following are the cases in which the values have a difference of exactly 1 1 .

( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 3 ) , ( 3 , 2 ) , ( 3 , 4 ) , ( 4 , 3 ) , ( 4 , 5 ) , ( 5 , 4 ) , ( 5 , 6 ) (1,2),(2,1),(2,3),(3,2),(3,4),(4,3),(4,5),(5,4),(5,6) and ( 6 , 5 ) (6,5) .

There are 10 10 cases. So the probability that Bob wins is 10 36 = \dfrac{10}{36}= 5 18 \boxed{\dfrac{5}{18}}

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