Question

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 1

`P(Somewhere) = 0.15`

`P(Elsewhere) = 0.3`

Step-by-step explanation:

Given

`P(Bedroom) = 0.4`

`P(kitchen) = 0.1`

`P(bathroom) = 0.2`

`P(livingroom) = 0.15`

Solving (a): Somewhere else

This is calculated as follows;

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

`P(Somewhere) = 1 - (P(bedroom) + P(kitchen) + P(bathroom) + P(living\ room))`

This gives:

`P(Somewhere) = 1 - (0.4 + 0.1 + 0.2 + 0.15)`

`P(Somewhere) = 1 - 0.85`

`P(Somewhere) = 0.15`

Solving (b): Bedroom or kitchen

This is calculated by adding individual probabilities

`P(Elsewhere) = P(Bedroom) + P(kitchen)`

`P(Elsewhere) = 0.2 + 0.1`

`P(Elsewhere) = 0.3`