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Question

# Bag A contains three red and four white Balls; bag B contains two red and three white balls. If one ball is drawn from bag A and two balls from bag B, find the probability that:(i) One ball is red and two balls are white;(ii) All the three balls are of the same colour.

A
i) 3370 and ii) 314
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B
i) 2231 and ii) 13
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C
i) 12 and ii) 12
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D
i) 825 and ii) 27
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Solution

## The correct option is A i) 3370 and ii) 314Possible selection are as follows(i) Red from bag A,2 white from bag B1 White from bag A,1 white from bag B1 Red from B∴ P(one ball is red and two balls are white)=3C17C1×3C25C2+4C17C1×3C1×2C15C2=37×310+47×3×210=910+2470=3370(ii) Possible selections are as follows1 Red from bag A,2 Red from bag B1 White from bag A,2 White from bag B∴ P(All the three balls are the same colour)=3C17C1×2C25C2+4C17C1×3C25C2=37×110+47×310=370+1270=1570=314

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