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We roll two fair 6-sided dice, A and B. Each one of the 36 possible outcomes is assumed to be equally likely.

1) Find the probability that dice A is larger than dice B.

2) Given that the roll resulted in a sum of 5 or less, find the conditional probability that the two dice were equal.

3) Given that the two dice land on different numbers, find the conditional probability that the two dice differed by 2.

 Feb 6, 2020
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1)  There are 15 rolls that result in A larger than B:  

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

     Probability  =  15/36.

 

2)  There are 10 rolls that result in a sum of 5 or less:   

      (4,1)    (3,2)    (2,3)    (1,4)    (3,1)    (1,3)    (2,2)    (2,1)    (1,2)    (1.,1)

     Two of these have dice that are equal.

      Probability  =  2/10.

 

3)  There are only 6 results that have both dice landing on the same number: 

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

      Therefore, there are 30 results that have different numbers.

      There are 8 results that have a difference of 2:  (6,4)    (4,6)    (5,3)    (3,5)    (4,2)    (2,4)    (3,1)    (1,3)

      Probability  =  8/30.

 Feb 6, 2020

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