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In a simultaneous throw of a pair of dice, find the probability of getting: neither 9 nor 11 as the sum of the numbers on the faces.

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78

18

16

56

answer is D.

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Detailed Solution

As given a simultaneous throw of a pair of dice.
So, let us find the probability of getting neither 9 nor 11 as the sum of the numbers on the faces.
The formula of the probability of neither

A

nor

B

P (A ∩ B) = 1 − P (A ∪ B)

The outcomes when a pair of dice is thrown simultaneously are: Question Image

Total number of outcomes is = 36
The outcomes for getting either 9 or 11 as the sum of number on the faces are

{(3, 6), (4, 5), (5, 4), (6, 3), (5, 6), (6, 5)}

.
So, number of outcomes for getting either 9 or 11 as the sum is = 6.
Probability of getting 9 or 11 as the sum of number on the faces is

⇒ P ′ = 636 ⇒ P ′ = 16

Therefore, the probability of getting neither 9 nor 11 as the sum of number on the faces is,

⇒ P = 1 − P ′ ⇒ P = 1 − 16 ⇒ P = 56

Therefore, probability of getting neither 9 nor 11 as the sum of numbers on faces is

56

.
Hence, option 4 is correct.

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