If P(A) = 0.7, P(B|A) = 0.3, P(A') = 0.1, and P(B|A') = 0.5, please calculate P(A|B) (round your answer to four decimal places) Also calculate P(B) (round your answer to four decimal places)AnswersP(A|B)::P(B)::SUBMIT ANSWER
Question
If P(A) = 0.7, P(B|A) = 0.3, P(A') = 0.1, and P(B|A') = 0.5, please calculate P(A|B) (round your answer to four decimal places) Also calculate P(B) (round your answer to four decimal places)AnswersP(A|B)::P(B)::SUBMIT ANSWER
Solution
First, let's calculate P(B). We can use the law of total probability, which states that P(B) = P(B|A)P(A) + P(B|A')P(A').
P(B) = P(B|A)P(A) + P(B|A')P(A') = 0.3 * 0.7 + 0.5 * 0.1 = 0.21 + 0.05 = 0.26
So, P(B) is approximately 0.26.
Next, let's calculate P(A|B). We can use Bayes' theorem, which states that P(A|B) = P(B|A)P(A) / P(B).
P(A|B) = P(B|A)P(A) / P(B) = 0.3 * 0.7 / 0.26 = 0.21 / 0.26 = 0.8077
So, P(A|B) is approximately 0.8077.
Therefore, the answers are:
P(A|B) = 0.8077 P(B) = 0.26
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