Homework SourseThe following data relate to the proportions in a population
The following data relate to the proportions in a population of drivers. A = [Accident in current year] B = [Defensive driver training last year] The probabilities are given in the accompanying Venn diagram. Find P(B|A). Round the answer to 4 decimal places. P(B | A) Are A and B independent? ![The following data relate to the proportions in a population of drivers. A = [Accident in current year] B = [Defensive driver training last year] The probabili](/WebImages/14/the-following-data-relate-to-the-proportions-in-a-population-1020619-1761527828-0.webp "The following data relate to the proportions in a population of drivers. A = [Accident in current year] B = [Defensive driver training last year] The probabili")
Solution
P(B|A) = P(A n B) / P(A)
As from the figure,
P(A n B) = 0.003
P(A) = 0.20 + 0.003 = 0.203
Then
P(B|A) = 0.014778325 [answer]
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If A and B are independent, P(B) = P(B|A).
As
P(B) = 0.003 + 0.05 = 0.053
which is not equal to P(B|A) above, then they are NOT INDEPENDENT.
