WJEC Maths for A2 – Applied

1.2 The conditional probability formula 17 Let the two events be A and B , so the events not happening will be A ′ and B ′. 2 Draw a tree diagram showing all the outcomes and probabilities given in the question. Use the tree diagram to multiply the probabilities along the path where the student doesn’t exercise regularly and is telling the truth that they don’t exercise regularly. This should equal 0.388 as given in the question. 3 For part (b) ϐind the branches using the tree diagram where the student is telling the truth. There are two paths to consider: P(Telling the truth) = P(Exercise regularly) × P(Telling the truth|Exercise regularly) + P(Don't exercise regularly) × P(Telling the truth|Don't exercise regularly) Converting to A and B notation: Pȍ B Ȏ = Pȍ A Ȏ × Pȍ B Ȏ + Pȍ A’  Ȏ × Pȍ B Ȏ Use the tree diagram to substitute numerical values in for each of these two paths. 4 In part (c), you want to ϐind the probability that the student regularly exercises ( A ) given that they are telling the truth ( B ) , so this is notated as P( A | B ). Use the conditional probability formula: P( A | B ) = Pȍ A ∩ B Ȏ Pȍ B Ȏ Multiply along the branch of your tree diagram to ϐind the probability that A and B both happen Pȍ A ∩ B Ȏ and then substitute this value into the formula. Answer (a) Let A = the event that a person claims to exercise regularly B = the event that the person is telling the truth A A Ԣ P( A ) = 0.60 P( A Ԣ ) = 0.40 P( B | A ) = 0.32 P( B Ԣ | A ) = 0.68 P( B | A Ԣ ) = 0.97 P( B Ԣ | A Ԣ ) = 0.03 B B Ԣ B B Ԣ Multiply along for ‘Claim don't exercise regularly’ and ‘Telling the truth given they don’t exercise regularly’. ȍ P( Claim don’t exercise regularly ) × P( Telling the truth|Claim don’t exercise regularly ) Ȏ should equal 0.388.