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In the town of Maplewood a certain type of DVD player is sold at just two stores. 36% of the sales are from store A and the rest of the sales are from store B. 7% of the DVD players sold at store A are defective while 3% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A

User Ccurves
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1 Answer

5 votes

Answer:

56.76% probability that it came from store A

Explanation:

Bayes Theorem:

Two events, A and B.


P(B|A) = (P(B)*P(A|B))/(P(A))

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
P(B) = 0.36

7% of the DVD players sold at store A are defective.

This means that
P(A|B) = 0.07

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


P(A) = 0.07*0.36 + 0.03*0.64 = 0.0444

What is the probability that it came from store A


P(B|A) = (0.36*0.07)/(0.0444) = 0.5676

56.76% probability that it came from store A

User Brijesh Singh
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