Scatterbrain Samantha often forgets to lock her house. This has caused the probability of a burglary to be 30%. If her house gets broken into, she faces a property loss of $10,000, otherwise she gets to keep her $100,000. What is her expected loss?

The question is missing the below options:

A $3000? B$10,000? C$30,000? D$100,000

The correct option is A, as expected loss is $3000 as computed below

Explanation:

The expected loss can be computed thus:

probability of theft*property loss of theft+probability of no theft*property loss of no theft

Probability of theft is 0.3 (30%)

probability of no theft 0.7 (1-0.3)

property loss of theft is $10000

property loss when no theft occur is $0

Expected loss=0.3*$10000+0.7*$0

expected loss=$3000+$0

expected loss=$3000

One needs to know that the entire probability of theft and no theft occurring is 1, so when one is given as 0.3, automatically the remainder belongs to other.