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Gloria or Dominic often misplaces a key that should be kept in the bedroom. The probability...

Gloria or Dominic often misplaces a key that should be kept in the bedroom. The probability that Gloria leaves the key in the kitchen is 0.3, and the probability that Dominic forgets it in the conservatory is 0.45. Gloria uses the key twice as frequently as Dominic.

(a) What is the probability that the key is in its proper place?

(b) Given that the key is not in the bedroom, what is the probability that Gloria has misplaced it?

Math   Statistics-And-Probability   
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