Probability
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Q.

When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11?

 A.

5/6

 B.

11/12

 C.

1/6

 D.

1/12

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Solution:
Option(B) is correct

Instead of finding the probability of this event directly, we will find the probability of the non-occurrence of this event and subtract it from 1 to get the required probability.

Combination whose sum of 12 is (6,6)

Combinations whose sum of 11 is (5,6), (6,5).

Therefore, there are totally 3 occurrences out of 36 occurrences that satisfy the given condition.

Probability whose sum of two numbers is greater than or equal to 11: 

\(=\dfrac{3}{36}=\dfrac{1}{12}\)

Hence probability whose sum of two numbers is lesser than 11: 

\(=1-\dfrac{1}{12}\)

\(=\dfrac{11}{12}\)


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