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Question
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
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Solution
Total number of balls = 10 + 15 = 25
Let S be event that two balls are drawn at random without replacement in succession
∴ n(S) = `""^25"C"_1xx""^24"C"_1` = 25 × 24
Let A be the event that the first ball is white and second is black.
First white ball can be drawn from 10 white balls in 10C1 ways and second black ball can be drawn from 15 black balls in 15C1 ways.
∴ n(A) = `""^10"C"_1xx""^15"C"_1`
∴ P(A) = `("n"("A"))/("n"("S"))=(""^10"C"_1xx""^15"C"_1) /(25xx24)=(10xx15)/(25xx24)=1/4`
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