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Question
A box contains 25 tickets numbered 1 to 25. Two tickets are drawn at random. What is the probability that the product on the numbers is even?
Solution
Two tickets can be drawn out of 25 tickets in 25C2 = `(25 xx 24)/(1 xx 2)` = 300 ways.
∴ n(S) = 300
Let A be the event that product of two numbers is even.
This is possible if both numbers are even, or one number is even, and other is odd.
As there are 13 odd numbers and 12 even numbers from 1 to 25.
∴ n(A) = `""^12"C"_1 + ""^12"C"_1 xx ""^13"C"_1`
= `(12 xx 11)/(1 xx 2) + 12 xx 13`
= 66 + 156
= 222
∴ Required probability = P(A)
= `("n"("A"))/("n"("S")`
= `222/300`
= `37/50`
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