Question Given that events A and B are independent with P(A)=0.7 and P(B)=0.46 determine the value of P(Avert B) ,rounding to the nearest thousandth, if necessary. Answer Attemptiout of

To determine the value of \( P(A \mid B) \), we need to use the definition of conditional probability. The formula for conditional probability is:<br /><br />\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} \]<br /><br />Since events A and B are independent, the probability of their intersection (both events happening) is the product of their individual probabilities:<br /><br />\[ P(A \cap B) = P(A) \times P(B) \]<br /><br />Given:<br />\[ P(A) = 0.7 \]<br />\[ P(B) = 0.46 \]<br /><br />We can calculate \( P(A \cap B) \):<br /><br />\[ P(A \cap B) = 0.7 \times 0.46 = 0.322 \]<br /><br />Now, we can find \( P(A \mid B) \):<br /><br />\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{0.322}{0.46} \approx 0.700 \]<br /><br />Therefore, the value of \( P(A \mid B) \) is approximately 0.700, rounded to the nearest thousandth.