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Question
A number of two digits is formed using the digits 1, 2, 3, ….., 9. What is the probability that the number so chosen is even and less than 60?
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Solution
The number of two digits can be formed from the given 9 digits in 9 × 9 = 81 different ways.
∴ n(S) = 81
Let A be the event that the number is even and less than 60.
Since the number is even, the unit place of two digits can be filled in 4P1 = 4 different ways by anyone of the digits 2, 4, 6, 8.
Also, the number is less than 60, so tenth place can be filled in 5P1 = 5 different ways by anyone of the digits 1, 2, 3, 4, 5.
∴ n(A) = 4 × 5 = 20
∴ Required probability = P(A) = `("n"("A"))/("n"("S")) = 20/81`
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