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Given P(A)=0.66,P(B)=0.3 and P(A and B)=0.248, find the value of P(A∣B), rounding to the nearest thousandth, if necessary. Answer:

Given P(A)=0.66,P(B)=0.3 P(A)=0.66, P(B)=0.3 and P(A P(A and B)=0.248 B)=0.248 , find the value of P(A∣B) P(A \mid B) , rounding to the nearest thousandth, if necessary.\newlineAnswer:

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Q. Given P(A)=0.66,P(B)=0.3 P(A)=0.66, P(B)=0.3 and P(A P(A and B)=0.248 B)=0.248 , find the value of P(A∣B) P(A \mid B) , rounding to the nearest thousandth, if necessary.\newlineAnswer:
  1. Use Formula: To find the conditional probability P(A∣B)P(A\mid B), we use the formula P(A∣B)=P(A and B)P(B)P(A\mid B) = \frac{P(A \text{ and } B)}{P(B)}. This formula represents the probability of event AA occurring given that event BB has occurred.
  2. Substitute Values: Substitute the given values into the formula: P(A∣B)=0.2480.3P(A\mid B) = \frac{0.248}{0.3}.
  3. Perform Division: Perform the division to find P(A∣B)P(A\mid B): P(A∣B)=0.2480.3≈0.826666....P(A\mid B) = \frac{0.248}{0.3} \approx 0.826666....
  4. Round Result: Round the result to the nearest thousandth: P(A∣B)≈0.827P(A\mid B) \approx 0.827.

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