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Conditional Probability

A fair dice i...

Question

A fair dice is thrown 3 times.The probability that the product of 3 outcomes is a prime number is ?

A

1/24

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B

1/36

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C

1/32

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D

1/8

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Solution

The correct option is A
1/24

Product is prime only when outcomes is (1,1,3) or (1,1,5) or(1,1,2) in all other cases it will be even.

1,1,3 can occur in 3 ways similarly for (1,1,2) and (1,1,5)

Favourable=9

Total ways: 216

P= $\frac{9}{216} = \frac{1}{24}$

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