Calculate P(A|B) given P(A intersect B) = 0.15 and P(B) = 0.35, and verify consistency with P(A|B) = 0.6.

let's tackle these questions.

Part (a): Probability

Given:
$P(A \cap B) = 0.15$
$P(B) = 0.35$
$P(A|B) = 0.6$

Note on consistency: The given values are inconsistent. If $P(A \cap B) = 0.15$ and $P(B) = 0.35$, then $P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.15}{0.35} = \frac{3}{7} \approx 0.42