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A man has mislaid his wallet. He thinks there is a 0.4 chance that the wallet is somewhere in his bedroom, a 0.1 chance it is in the kitchen, a 0.2 chance it is in the bathroom, and a 0.15 chance it is in the living room. What is the probability that the wallet is a) somewhere else? b) in either the bedroom or the kitchen?

Answer :

MrRoyal

Answer:

[tex]P(Somewhere) = 0.15[/tex]

[tex]P(Elsewhere) = 0.3[/tex]

Explanation:

Given

[tex]P(Bedroom) = 0.4[/tex]

[tex]P(kitchen) = 0.1[/tex]

[tex]P(bathroom) = 0.2[/tex]

[tex]P(livingroom) = 0.15[/tex]

Solving (a): Somewhere else

This is calculated as follows;

Because it is not in any of the given places; the probability is calculated as:

[tex]P(Somewhere) = 1 - (P(bedroom) + P(kitchen) + P(bathroom) + P(living\ room))[/tex]

This gives:

[tex]P(Somewhere) = 1 - (0.4 + 0.1 + 0.2 + 0.15)[/tex]

[tex]P(Somewhere) = 1 - 0.85[/tex]

[tex]P(Somewhere) = 0.15[/tex]

Solving (b): Bedroom or kitchen

This is calculated by adding individual probabilities

[tex]P(Elsewhere) = P(Bedroom) + P(kitchen)[/tex]

[tex]P(Elsewhere) = 0.2 + 0.1[/tex]

[tex]P(Elsewhere) = 0.3[/tex]

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