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If two dice and one coin is rolled and tossed simultaneously, then find the probability that the coin shows head and the numbers on the top faces of the dice are not same?

If two dice and one coin is rolled and tossed simultaneously, then find the probability that the coin shows head and the numbers on the top faces of the dice are not same? Correct Answer 5 / 12

GIVEN:

Two dice and one coin are rolled & tossed simultaneously

CONCEPT:

Probability of getting head or tail in a coin = 1 / 2

Probability = Number of favorable case / Total cases

CALCULATION:

Probability of getting head = 1 / 2

When two dice are rolled, cases when same number on the face of both dice:

(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

Now,

Probability of not getting same number on the face of both dice = 1 – 6 / 36 = 5 / 6

∴ Required probability = 1 / 2 × 5 / 6 = 5 / 12 

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