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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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