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In: Statistics and Probability

suppose you rolled a pair of dice. what is the probability of not getting a sum...

suppose you rolled a pair of dice. what is the probability of not getting a sum of 7 or 8?

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Expert Solution

probability of not getting a sum of 7 or 8 = 1 - probability of getting a sum of 7 or 8

Let X denotes the sum of the roll of two die

Probability of not getting a sum of 7 or 8 = 1 - P[ X = 7 ] - P[ X = 8 ]

Total number of cases on the roll of two die = 36

Number of cases where the sum on die is 7 = (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 cases

Number of cases where the sum on die is 8 = (2,6), (3,5), (4,4), (5,3), (6,2) = 5 cases

P[ X = 7 ] = Number of cases where the sum on die is 7 / Total number of cases on the roll of two die

P[ X = 7 ] = 6/36 = 1/6

P[ X = 8 ] = Number of cases where the sum on die is 8 / Total number of cases on the roll of two die

P[ X = 8 ] = 5/36

Probability of not getting a sum of 7 or 8 = 1 - P[ X = 7 ] - P[ X = 8 ]

Probability of not getting a sum of 7 or 8 = 1 - (6/36) - (5/36)

Probability of not getting a sum of 7 or 8 = 1 - (11/36)

Probability of not getting a sum of 7 or 8 = 25/36

Probability of not getting a sum of 7 or 8 = 0.6944

orchestra answered 2 years ago
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