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A die is loaded so that the probability of face i is proportional to i, i=1,2,...6 . The probability of an even number occurring when die is rolled $\frac{k}{7}$ . Find the value of k.

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Detailed Solution

The faces ondie are proportional to the numbers on them

1 = k, 2 = 2 k, 3 = 3 k, 4 = 4 k, 5 = 5 k, b = 6 k

k + 2 k = 3 k + 4 k + 5 k + 6 k = 1

21 k = 1

k = \frac{1}{21}

Probability of even

2 k + 4 k + 6 k = 12 k

Hence the value of k is 4

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