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  • An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: C: the sum is at least 7 and a multiple of 3

3.     An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

        C: the sum is at least 7 and a multiple of 3

Answers (1)

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Sample space when a die is rolled:

S = {1, 2, 3, 4, 5, 6}

Let E = Event of rolling a pair of dice (= Event that a die is rolled twice!) [6x6 = 36 possible outcomes]

E = [ {(x,y): x,y \dpi{100} \in S } ] = {(1,1), (1,2)...(1,6),(2,1).....(6,5),(6,6)}

Now,

C: the sum is at least 7 and a multiple of 3

The sum can only be 9 or 12.

C = [ {(a,b): (a,b) \dpi{100} \in E, a+b>6 & a+b = 3k, k \dpi{100} \in I} ]= {(3,6), (6,3), (5, 4), (4,5), (6,6)}

Posted by

HARSH KANKARIA

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