WJEC Maths for A2 – Applied

1.3 Use of Venn diagrams for conditional probability 19 Answer 1 (a) P( A ) = 0.55 + 0.1 = 0.65 (b) P( A only) = 0.55 (c) P( A ∩ B ) = 0.1 (d) P( A ∪ B ) = 0.55 + 0.1 + 0.2 = 0.85 (e) P( A ′ ∩ B ) = 0.2 In this section we will look at how we use Venn diagrams to solve problems involving conditional probability. Suppose we have two events A and B . The probability of B occurring may change depending on whether event A has occurred or not. B A S As event A has occured, we only consider the probabilities in set A , i.e. P ( A ). B A S This region represents B occurring given that A has occurred. Example 1 A and B are two events such that Pȍ A | B  Ȏ = 0.3, Pȍ A | B′  Ȏ = 0.2 and Pȍ B  Ȏ = 0.25 Find: (a) P( A ∩ B  ) (b) P( A ∩ B′  ) (c) P( A ) (d) P( B | A ) (e) P( B | A ’) (f) P( B′  | A′  ) Answer 1 (a) P( A | B ) = Pȍ A ∩ B Ȏ Pȍ B Ȏ So, Pȍ A ∩ B Ȏ = Pȍ A | B Ȏ × Pȍ B  Ȏ = 0.3 × 0.25 = 0.075