Question
Given that events A and B are independent with P, left parenthesis, A, right parenthesis, equals, 0, point, 6, 3P(A)=0.63 and P, left parenthesis, B, vertical bar, A, right parenthesis, equals, 0, point, 3P(B∣A)=0.3, determine the value of P, left parenthesis, B, right parenthesisP(B), rounding to the nearest thousandth, if necessary.
Answer
A
Answer
A
Answers
Answered by
GPT-4o mini
To solve for \( P(B) \), we can use the concept of independence and the properties of conditional probability.
1. Given that the events \( A \) and \( B \) are independent, we have:
\[
P(B | A) = P(B)
\]
2. We are also given:
- \( P(A) = 0.63 \)
- \( P(B | A) = 0.3 \)
Since \( P(B | A) = P(B) \) and we know \( P(B | A) = 0.3 \), we can directly conclude that:
\[
P(B) = P(B | A) = 0.3
\]
Thus, the value of \( P(B) \) is \( \boxed{0.3} \).
1. Given that the events \( A \) and \( B \) are independent, we have:
\[
P(B | A) = P(B)
\]
2. We are also given:
- \( P(A) = 0.63 \)
- \( P(B | A) = 0.3 \)
Since \( P(B | A) = P(B) \) and we know \( P(B | A) = 0.3 \), we can directly conclude that:
\[
P(B) = P(B | A) = 0.3
\]
Thus, the value of \( P(B) \) is \( \boxed{0.3} \).
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