Two dice are thrown :
$P$ is the event that the sum of the scores on the uppermost faces is a multiple of $6$ .
$Q$ is the event that the sum of the scores on the uppermost faces is at least $10$ .
$R$ is the event that same scores on both dice.
Which of the following pairs is mutually exclusive?

P, Q

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P, R

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Q, R

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None of these

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Solution

The correct option is C None of these
Possibilities of $P$ , $(3, 3), (6, 6), (1, 5), (5, 1), (4, 2), (2, 4)$
Possibilities of $Q : (5, 5), (5, 6), (6, 5), (6, 6)$
Possibilities of $R : (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)$
Thus, the possibilities are neither exhaustive, nor mutually exclusive nor these are complementary probabilities.

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R is the event that same score on both dice.

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