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Mathematics

Assertion (A) : A dice is rolled two times the probability of getting an odd number on each dice is 14\dfrac{1}{4}.

Reason (R) : The favourable outcomes are (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3) and (5, 6).

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Probability

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Answer

Given,

A dice is rolled two times.

Possible outcomes = {(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)}.

Number of total outcomes = 36

Favourable outcomes (for getting odd number on both dice) = {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)}

So, reason (R) is false.

Number of favourable outcomes = 9

Probability = Number of favourable outcomesNumber of total outcomes=936=14\dfrac{\text{Number of favourable outcomes}}{\text{Number of total outcomes}} = \dfrac{9}{36} = \dfrac{1}{4}.

So, assertion (A) is true.

∴ A is true, but R is false.

Hence, option 3 is the correct option.

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