Call a household prosperous if its income exceeds $100,000. Call the household e
ID: 3277524 • Letter: C
Question
Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to a survey,
P(A) = 0.137, P(B) = 0.273,
and the probability that a household is both prosperous and educated is
P(A and B) = 0.083.
What is the conditional probability that a household is prosperous, given that it is educated? (Round your answer to four decimal places.)
Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to a survey, P(A) = 0.137, P(B) = 0.273, and the probability that a household is both prosperous and educated is P(A and B) = 0.083. What is the conditional probability that a household is prosperous, given that it is educated? (Round your answer to four decimal places. ) Explain why your result shows that events A and B are not independent. O If A and B were independent, then P(AIB) would equal PCB), and P(A and B) would equal the sum P(a) + P(B). O If A and B were independent, then PAIB) would equal PIA), and PA and B) would equal the product PCA)P(B). O If A and B were independent, then P(AIB) would equal P(A), and P(A and B) would equal the sum P(a) + P(B). O If A and B were independent, then P(AIB) would equal PA and B), and PA and B) would equal the product P(APB). O If A and B were independent, then P(AIB) would equal PCB), and PA and B) would equal the product P(AP(B).Explanation / Answer
probability that a household is prosperous given that it is educated =P(A|B)=P(AnB)/P(B)=0.083/0.273=0.3040
2nd option is correct:
if A and B were independent ; then P(A|B) would equal P(A) and P(A and B) would equal the product P(A)P(B)
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