If two different dice are rolled together, the probability of getting an even number on both dice is:

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Solution

Solve for the favorable outcomes and find the required probability:
Possible outcomes of rolling the two dice 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 $= 36$
The favorable outcomes are:
${(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)} .$
Total number of favorable outcomes $= 9$
Probability of getting an even number on both dice $= \frac{9}{36} = \frac{1}{4}$
Hence, the probability of getting an even number on both dice is $\frac{1}{4}$

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Similar questions

Q. Mark the correct alternative in each of the following:

If two different dice are rolled together, the probability of getting an even number on both dice is

(a)

\frac{1}{36}

(b)

\frac{1}{2}

(c)

\frac{1}{6}

(d)

\frac{1}{4}

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