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A dice is loaded so that the probability...

A dice is loaded so that the probability of a face I is proportional to `i^(2)` , I = 1, 2, …, 6. Then find the probability of occurring a prime number when the dice is rolled.

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The correct Answer is:
`(4)/(7)`
Since the probabilities of the faces are proportional to the numbers on them, we can take the probailities of faces 1, 2, …, 6 as k, 2k, …, 6k, respectively. Since one of the faces must occur, we have k + 2k + 3k + 4k + 5k + 6k = 1 or k = `1//21`
Therefore, the probability of occurence of an even number is 2k + 4k + 6k = 12k = 12/21 = 4/7.
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