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Question

A die is loaded so that the probability of a face i is proportional to i, i=1,2,...6. The probability of an even number occurring when the die is rolled is b7, the value of b is

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Solution

Since the probability of the faces are proportional to the numbers on them, we can take the probabilities 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=1k=121
Therefore, the probability of occurence of an even number is 2k+4k+6k=12k=1221=47

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