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What is the probability of getting a sum of 7 on rolling a pair of dice?

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\frac{5}{9}

\frac{2}{3}

\frac{1}{4}

\frac{1}{6}

answer is D.

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Detailed Solution

Given, a pair of dice is rolled.
The P(A) of the random experiment is,

P (A) = \frac{Number of favorable outcomes}{Total number of outcomes}

The possible outcomes when 2 dies are rolled are:

(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 number of outcomes = 36.
From the sample space, the events where we get a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1).
Number of favorable outcomes = 6
Thus, the probability is,

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

\Rightarrow P (E) = \frac{6}{36}

\Rightarrow P (E) = \frac{1}{6}

Therefore, the required probability is

\frac{1}{6}

.
Hence, option 4 is the correct answer.

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