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Question

In a simultaneous throw of a pair of dice, if the probability of getting neither 9 nor 11 as the sum of the numbers on the faces is 5a. Find a.

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Solution

The outcomes that we gets, in a simultaneous throw of a pair of dice are,

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)⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪

n(S)=36

Now,
Favourable outcomes i.e getting neither 9 nor 11 as the sum of numbers on the faces are

E=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪(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)(4,1)(4,2)(4,3)(4,4)(4,6)(5,1)(5,2)(5,3)(5,5)(6,1)(6,2)(6,4)(6,6)⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪

n(E)=30

P(E)=n(E)n(S)=3036

P(E)=56=5a

a=6

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