WLD Incorporated, a national data-collection agency, estimates that 52% of all customers at home warehouse stores (in the United States) own their own home. WLD also estimates that 43% of all home warehouse customers have lived at their current address for less than five years, and that 41% of all home warehouse customers both own their own home and have lived at their current address for less than five years. Using these estimates, what is the probability that a randomly selected home warehouse customer owns her own home or has lived at her current address for less than five years (or both)?Write your answer as a decimal
Question
WLD Incorporated, a national data-collection agency, estimates that 52% of all customers at home warehouse stores (in the United States) own their own home. WLD also estimates that 43% of all home warehouse customers have lived at their current address for less than five years, and that 41% of all home warehouse customers both own their own home and have lived at their current address for less than five years. Using these estimates, what is the probability that a randomly selected home warehouse customer owns her own home or has lived at her current address for less than five years (or both)?Write your answer as a decimal
Solution
To solve this problem, we need to use the formula for the probability of the union of two events, which is P(A U B) = P(A) + P(B) - P(A ∩ B).
Here, event A is the event that a customer owns their own home, and event B is the event that a customer has lived at their current address for less than five years.
From the problem, we know that:
P(A) = 0.52 (the probability that a customer owns their own home) P(B) = 0.43 (the probability that a customer has lived at their current address for less than five years) P(A ∩ B) = 0.41 (the probability that a customer both owns their own home and has lived at their current address for less than five years)
Substituting these values into the formula gives us:
P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.52 + 0.43 - 0.41 = 0.54
So, the probability that a randomly selected home warehouse customer owns her own home or has lived at her current address for less than five years (or both) is 0.54.
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