WJEC Maths for A2 – Applied

1 Probability 12 (b) Using your tree diagram, ϐind: (i) P( A ∩ B ) (ii) P( A′ ∩ B′  ) (iii) P( B′  | A ) Answer 1 (a) A A Ԣ P( A ) = 0.4 P( A Ԣ ) = 0.6 P( B | A ) = 0.7 P( B Ԣ | A ) = 0.3 P( B | A Ԣ ) = 0.4 P( B Ԣ | A Ԣ ) = 0.6 B B Ԣ B B Ԣ (b) (i) P( A ∩ B ) = P( A ) × P( B | A ) = 0.4 × 0.7 = 0.28 (ii) P( A′ ∩ B′  ) = P( A′  ) × P( B′  | A′  ) = 0.6 × 0.6 = 0.36 (iii) P( B′  | A ) = 0.3 2 Two events A and B occur such that P( B | A ) = 0.55, P( B  | A′  ) = 0.5 and P( A ) = 0.65 (a) Draw a tree diagram to represent this information. (b) Find the following probabilities (i) P( A ∩ B ) (ii) P( B ) (iii) P( A | B ) Answer 2 (a) A A Ԣ P( A ) = 0.65 P( A Ԣ ) = 0.35 P( B | A ) = 0.55 P( B Ԣ | A ) = 0.45 P( B | A Ԣ ) = 0.5 P( B Ԣ | A Ԣ ) = 0.5 B B Ԣ B B Ԣ It is a good idea to write the probability in full rather than just the number on each of the branches, e.g. rather than write 0.4 on the branch for A , you would write P( A ) = 0.4. It takes a bit longer but is helpful when you have to work out probabilities. BOOST G ra d e ⇪⇪⇪⇪