For customers purchasing a refrigerator at a certain appliance store, let A be t

Question

For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are P(A) = 0.75, P(B|A) = 0.9 P(B | A^c) = 0.8, P(C | A intersection B) = 0.8, P(C | A intersection B^c) = 0.6, P(C | A^c intersection B) = 0.7, P(C | A^c intersection B^c) = 0.3. Find P(A intersection B); P(A intersection B intersection C); P(A^c intersection B);

Explanation / Answer

Answer:

We know that P(B/A) = P(A B) / PA

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

= 0.75 * 0.9 = 0.675

We know that P( C / A B ) = P( A B C ) / P( A B)

=> P(A B C) = P( C/A B) * P(A B) = 0.8 * 0.675 = 0.54

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