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Question
Solve the following:
Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is and even number?
Solution
If one card is drawn from the box, the sample space S is given by
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
∴ n(S) = 10
It is given that number on the card is more than three
∴ the sample space reduces to A= {4, 5, 6, 7, 8, 9, 10}
∴ n(A) = 7
∴ Let B ≡ the event of drawing an even number
∴ B = {2, 4, 6, 8, 10}
∴ A ∩ B = {4, 6, 8, 10}
∴ n(A ∩ B) = 4
∴ The required probability = `"P"("B"/"A")`
= `("n"("A" ∩ "B"))/("n"("A"))`
= `4/7`
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