Double roll

Number Theory Level 2

A dice is rolled twice.

Find the probability of getting a two on just one of these throws.

1 2 \frac{1}{2} 19 36 \frac{19}{36} 1 12 \frac{1}{12} 5 18 \frac{5}{18}

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

Tom Engelsman
Aug 15, 2019

There are 6 2 = 36 6^2 = 36 ordered-pair outcomes for two consecutive rolls of this fair die. If we are interested when only one '2' appears, then the desired outcomes are:

( 1 , 2 ) ; ( 2 , 1 ) ; ( 3 , 2 ) ; ( 2 , 3 ) ; ( 4 , 2 ) ; ( 2 , 4 ) ; ( 5 , 2 ) ; ( 2 , 5 ) ; ( 6 , 2 ) ; ( 2 , 6 ) (1,2); (2,1); (3,2); (2,3); (4,2); (2,4); (5,2); (2,5); (6,2); (2,6)

which is ten total outcomes. Thus the required probability equals 10 36 = 5 18 . \frac{10}{36} = \boxed{\frac{5}{18}}.

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