an article appears in a news paper stating that 40 of homeow

an article appears in a news paper stating that 40% of homeowners in a certain community have mortgages that are \"underwater\". In that same community 19% of the homeowners are unemployed or underemployed. Lasly, 3% of tr homeowners find themselves in both situations: homeowners with underwater mortgages and also unemployed or underemployed.

If a homeowner is chosen at random from this population, what is the probability that:

a) this person is unemployed/ underemployed or with an underwater mortgage.

b) this person is neither unemployed/ underemployed nor with an under water mortgage.

c) that this person is unemployed/underemployed but the mortgage is not under water.

also: If a homeowner that is neither unemployed/under employed is chosen at random, what is the probability that the mortgage is under water?

Thanks a million!!!

Solution

Given P(underwater) = 0.4

P(unemployed or underemployed) =0.19

P(homeowners with underwater mortgages and also unemployed or underemployed) =0.03

a) this person is unemployed/ underemployed or with an underwater mortgage.

P(unemployed/ underemployed or with an underwater mortgage)

=P(unemployed/ underemployed) + P(underwater mortgage) - P(both)

=0.19+0.4 -0.03

=0.56

---------------------------------------------------------------------------------------------------------------------------------

b) this person is neither unemployed/ underemployed nor with an under water mortgage.

P(neither unemployed/ underemployed nor with an under water mortgage)

= 1-0.56

=0.44

---------------------------------------------------------------------------------------------------------------------------------

c) that this person is unemployed/underemployed but the mortgage is not under water.

P(unemployed/underemployed but the mortgage is not under water)

=P(unemployed/underemployed) - P(both)

=0.19 - 0.03

=0.16

---------------------------------------------------------------------------------------------------------------------------------

also: If a homeowner that is neither unemployed/under employed is chosen at random, what is the probability that the mortgage is under water?

P(under water | neither unemployed/under employed)

=P(under water and neither unemployed/under employed)/P(neither unemployed/under employed)

= (0.4-0.03)/(1-0.19)

=0.4567901