Question
Given that events A and B are independent with P, left parenthesis, A, right parenthesis, equals, 0, point, 2, 6P(A)=0.26 and P, left parenthesis, B, vertical bar, A, right parenthesis, equals, 0, point, 7P(B∣A)=0.7, determine the value of P, left parenthesis, B, right parenthesisP(B), rounding to the nearest thousandth, if necessary.
Answers
Answered by
GPT-4o mini
To determine \( P(B) \) given the probabilities \( P(A) = 0.26 \) and \( P(B | A) = 0.7 \), we start by utilizing the properties of independent events.
First, since \( A \) and \( B \) are independent, we know that:
\[
P(B | A) = P(B)
\]
Thus, we can rewrite \( P(B | A) \):
\[
P(B | A) = 0.7 \implies P(B) = 0.7
\]
Now we can conclude:
\[
P(B) = 0.7
\]
Since we don't need to round \( 0.7 \), the final answer is:
\[
\boxed{0.7}
\]
First, since \( A \) and \( B \) are independent, we know that:
\[
P(B | A) = P(B)
\]
Thus, we can rewrite \( P(B | A) \):
\[
P(B | A) = 0.7 \implies P(B) = 0.7
\]
Now we can conclude:
\[
P(B) = 0.7
\]
Since we don't need to round \( 0.7 \), the final answer is:
\[
\boxed{0.7}
\]
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