Calculate P(B) given P(A' ∩ B) = 1/7 and P(A ∩ B) = 2/9.

Here's the solution to question 1:

1. (i) Events A and B
Given:
$P(A' \cap B) = \frac{1}{7}$
$P(A \cap B) = \frac{2}{9}$

a) Calculate $P(B)$
The event B can be expressed as the union of two disjoint events: $(A \cap B)$ and $(A' \cap B)$.
Therefore, $P(B) = P(A \cap B) + P(A' \cap B)$.

$$P(B) = \frac{2}{9} + \frac{1}{7}$$

To add these fractions, find a common denominator, which is $