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When three fair dice are thrown simultaneously, what is the probability that the first die shows up an even number, the second die shows up an even prime number and the third die shows up a composite number? 

When three fair dice are thrown simultaneously, what is the probability that the first die shows up an even number, the second die shows up an even prime number and the third die shows up a composite number?  Correct Answer 1/36

Calculation:

Let A: the event of the first die showing up an even number, 2, 4, or 6.

B: the event of the second die showing up an even prime number, 2.

C: the event of the third die showing up a composite number 4 or 6.

Their respective probabilities being,

⇒ P(A) = 3/6 = 1/2, P(B) = 1/6, and P(C) = 2/6 = 1/3

The require probability is obtained by compounding these events by multiplying individual probabilities.

Hence the require probability = 1/2 × 1/6 × 1/3 = 1/36

∴ The required result will be 1/36.

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