The events A and B are such that P(A) = 0.7, P(B) = 0.5 and P(A ∩ B) = 0.3 - Leaving Cert Mathematics - Question 1 - 2012

To find the conditional probability of A given B, we use the formula:

$P(A | B) = \frac{P(A ∩ B)}{P(B)}$

Substituting the known values:

$P(A | B) = \frac{0.3}{0.5} = 0.6$

Hence, the conditional probability P(A | B) is 0.6.

Two events A and B are considered independent if:

$P(A ∩ B) = P(A) \cdot P(B)$

Calculating the right side:

$P(A) \cdot P(B) = 0.7 \cdot 0.5 = 0.35$

Given that P(A ∩ B) = 0.3, we can see that:

$0.3 \neq 0.35$

Thus, A and B are not independent events, as their intersection probability does not equal the product of their individual probabilities.