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Question

# An expert burglar has 8 master keys to open several new houses of a mansion.Only one master key will open a given house.If 40% of these houses remain unlocked the probability that the burglar will break open the treasury house on selecting 3 master keys at random is?

A

5/8

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B

2/8

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C

3/5

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D

3/4

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Solution

## The correct option is A 5/8 X: Home is unlocked=P(X)=25 Y:Home is locked:P(Y)=35 Z: Room gets opened by any of the 3 keys P(Z)=P(Z intersection X)+P(Z intersection Y) P(Z)=P(X)×P(ZX)+P(Y)×P(ZY) P(Z)=25+35×P(ZY) P(ZY)=7C28C3=38 Hence P(Z)=25+(35×38)=58

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