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

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\frac{11}{12}

\frac{1}{12}

\frac{2}{12}

\frac{1}{8}

answer is A.

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Detailed Solution

Given: two dice are thrown.
To find: the probability that the sum of the two numbers that turn up is less than

11

According to the question

n (S) = 6 \times 6 = 36

Favourable outcomes for sum less than

11

is:

{(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),

(6, 1), (6, 2), (6, 3), (6, 4)}

\Rightarrow n (E) = 33

Probability

P (E) = \frac{n (E)}{n (S)}

.
Hence, the probability of getting a total less than

11

P (E) = \frac{33}{36}

P (E) = \frac{11}{12}

Therefore, option (1) is correct.

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