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A Bag Contains 5 White and 4 Black Balls and Another Bag Contains 7 White and 9 Black Balls. a Ball is Drawn from the First Bag and Two Balls Are Drawn from the Second Bag. - Mathematics

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Sum

A bag contains 5 white and 4 black balls and another bag contains 7 white and 9 black balls. A ball is drawn from the first bag and two balls are drawn from the second bag. What is the probability of drawing one white and two black balls? 

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Solution

Bag I Bag II
4B 7W
5W 9B
Total balls in bag I = 9 Total balls in bag II = 16

Required probability = `(5/9) ((""^9C_2)/(""^16C_2)) + (4/9) (( ""^7 C_1 xx ""^9C_1)/(""^16C_2))`

= `(5)/(9) xx (9xx8)/(16xx15) + (4)/(9) xx (7xx9)/( 8xx 15)`

= `(1)/(6) + (7)/(30) = (5+7)/(30) = (12)/(30) = (2)/(5)`.

Concept: Multiplication Theorem on Probability
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