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If the probability that the product of t...

If the probability that the product of the outcomes of three rolls of a fair dice is a prime number is `p ,` then the value of `1//(4p)` is_____.

Text Solution

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Total number of cases n(S) = `6^(3) = 216`
Product is prime only when two outcomes are 1 and the third is prime, i.e., 2, 3, 5.
If it is 2, 1, 1, then the number of cases is 3.
Similarly, 3 cases for 3, 1, 1 and 5, 1, 1 each
Hence, required probability `p = (1)/(24)`
`implies (1)/(4p) = 6`
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