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Question

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In a simultaneous throw of a pair of dice, the probability of getting a sum more than 7 is 512.

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Solution

The outcomes that we get on a simultaneous throw of a pair of dice is:

S=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
Total no. of possible outcomes are 36

Let E be the event of getting a sum more than 7

Favorable outcomes are:
O=[(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)]
No. of favourable outcomes are 15

We know that,
P(E)=No. of favourable outcomestotal no. of possible outcomes
P(E)=1536=512


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