Respuesta :
Answer:
56.76% probability that it came from store A
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Defective.
Event B: Store A.
36% of the sales are from store A
This means that [tex]P(B) = 0.36[/tex]
7% of the DVD players sold at store A are defective.
This means that [tex]P(A|B) = 0.07[/tex]
Probability of a defective DVD:
36% come from store A, and of those, 7% are defective.
100 - 36 = 64% come from store B, and of those, 3% are defective. So
[tex]P(A) = 0.07*0.36 + 0.03*0.64 = 0.0444[/tex]
What is the probability that it came from store A
[tex]P(B|A) = \frac{0.36*0.07}{0.0444} = 0.5676[/tex]
56.76% probability that it came from store A
