Probability Calculation: Finding P(B|A)

The problem asks for the conditional probability $P(B|A)$. We are given the probabilities $P(A)$, $P(B)$, and $P(A \cup B)$.

Conditional Probability Formula

The formula for conditional probability is:

$ P(B|A) = \frac{P(A \cap B)}{P(A)} $

To use this formula, we first need to determine the probability of the intersection of events A and B, $P(A \cap B)$.

Calculating Intersection Probability P(A ∩ B)

We can find $P(A \cap B)$ using the formula for the probability of the union of two events:

$ P(A \cup B) = P(A) + P(B) - P(A \cap B) $

Rearranging this formula to solve for $P(A \cap B)$ gives:

$ P(A \cap B) = P(A) + P(B) - P(A \cup B) $

Substitute the given values:

$ P(A \cap B) = 0.6 + 0.2 - 0.7 $

$ P(A \cap B) = 0.8 - 0.7 $

$ P(A \cap B) = 0.1 $

Calculating Conditional Probability P(B|A)

Now, substitute the value of $P(A \cap B)$ and the given $P(A)$ into the conditional probability formula:

$ P(B|A) = \frac{P(A \cap B)}{P(A)} $

$ P(B|A) = \frac{0.1}{0.6} $

Simplify the fraction:

$ P(B|A) = \frac{1}{6} $

Thus, the conditional probability $P(B|A)$ is $1/6$.