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Question
One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that one white and one black
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Solution
First Bag contains 5 white and 3 black balls
Total number of balls in the first bag 8 Second Bag contains 4 white and 6 black halls
Total number of balls in the second bag = 10
One ball is drawn from each bag.
P(getting one white and one black) = P( getting one white from the first bag or one white from the second bag) + P(getting one black from the first bag or one black from the second bag)
= `((""^5"C"_1)/(""^8"C"_1) xx (""^6"C"_1)/(""^10"C"_1)) + ((""^4"C"_1)/(""^10"C"_1) xx (""^3"C"_1)/(""^8"C"_1))`
= `(5/8 xx 6/10) + (4/10 xx 3/8)`
= `3/8 + 3/20`
= `(15 + 6)/40`
= `21/40`
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