Question

WLD Incorporated, a national data-collection agency, estimates that 60% of all customers at home warehouse stores (in the United States) own their own home. WLD also estimates that 54% of all home warehouse customers have lived at their current address for less than five years, and that 71% of all home warehouse customers own their own home or have lived at their current address for less than five years (or both). Using these estimates, what is the probability that a randomly selected home warehouse customer both owns her own home and has lived at her current address for less than five years

Answer 1

`P(W\ n\ F) = 43\%`

Explanation:

Given

Represent customers that own their homes with W

Represent customers that have lived for less than 5 years with F

Such that:

`P(W) = 60\%`

`P(F) = 54\%`

`P(W\ or\ F) = 71\%`

Required

Determine
`P(W\ n\ F)`

In Probability:

`P(W\ or\ F) = P(W) + P(F) - P(W\ n\ F)`

Substitute values for each

`71\% = 60\% + 54\% - P(W\ n\ F)`

`71\% = 114\% - P(W\ n\ F)`

Solve for P(W n F)

`P(W\ n\ F) = 114\% - 71\%`

`P(W\ n\ F) = 43\%`