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A fair coin is tossed and a fair die is rolled simultaneously. Find the probability that the die shows an odd prime number and the coin shows a tail.

A fair coin is tossed and a fair die is rolled simultaneously. Find the probability that the die shows an odd prime number and the coin shows a tail. Correct Answer 1/6

Given:

A coin is tossed and a die is rolled. 

Calculation:

Let H be the head and T be the tail of the coin.
⇒ S = { (1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)}

⇒ n(S) = 12
Let E be the event " the die shows an odd prime number and the coin shows a tail ".

Event E may be described as follows

⇒ E = {(3, T), (5, T)}

⇒ n(E) = 2

The probability P(E) is given by

⇒ P(E) = n(E)/n(S) = 2/12 = 1/6

∴ Required probability = 1/6

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