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Question
Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a nonprime number. The probability that the card was drawn from Box I is ______.
Options
`4/17`
`8/17`
`2/5`
`2/3`
Solution
Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a nonprime number. The probability that the card was drawn from Box I is `underlinebb(8/17)`.
Explanation:
P(Box I) = `1/2`
P(Box II) = `1/2`
`"P"(("Non Prime")/("Box" "I")) = 20/30`
`"P"(("Non Prime")/("Box" "II")) = 15/20`
`"P"(("Box" "I")/("Non Prime")) = (1/2 xx 20/30)/(1/2 xx 20/30 + 1/2 xx 15/20) = 8/17`
