Question
2. The following are probabilities for an experiment in which \( A \) and \( B \) are two possible events. \( P(A \cap B)=0.21 \), and \( P(A)=0.7 \). Find \( P(B \mid A) \).
Ask by Chavez Bond. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( P(B \mid A) = 0.3 \)
Solution
We are given that P(A ∩ B) = 0.21 and P(A) = 0.7. The conditional probability P(B | A) is defined as the probability of B occurring given that A has occurred, and is computed as:
P(B | A) = P(A ∩ B) / P(A)
Substitute the given values:
P(B | A) = 0.21 / 0.7 = 0.3
Thus, the probability P(B | A) is 0.3.
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Simplify this solution Extra Insights
To find \( P(B \mid A) \), we can use the formula for conditional probability: \[ P(B \mid A) = \frac{P(A \cap B)}{P(A)}. \] Given that \( P(A \cap B) = 0.21 \) and \( P(A) = 0.7 \), we can substitute these values into the formula: \[ P(B \mid A) = \frac{0.21}{0.7} = 0.3. \] Thus, \( P(B \mid A) = 0.3 \).
