WJEC Maths for A2 – Applied

1.2 The conditional probability formula 13 (b) (i) P( A ∩ B ) = P( A ) × P( B | A ) = 0.65 × 0.55 = 0.3575 (ii) P( B ) = P( A ) × P( B | A ) + P( A′  ) × P( B | A′  ) = 0.65 × 0.55 + 0.35 × 0.5 = 0.5325 (iii) P( A | B ) = Pȍ A ∩ B Ȏ Pȍ B Ȏ = 0.3575 0.5325 = 0.6714 3 When Ahmed travels to college by car, the probability of him being late is 0.2. If he does not travel by car, the probability of him being late is 0.3. The probability of him travelling by car is 0.4. Find the probability that Ahmed is late. Answer 3 Let C = event that Ahmed travels by car. L = event that Ahmed is late. C C Ԣ P( C ) = 0.4 P( C Ԣ ) = 0.6 P( L | C ) = 0.2 P( L Ԣ | C ) = 0.8 P( L | C Ԣ ) = 0.3 P( L Ԣ | C Ԣ ) = 0.7 L L Ԣ L L Ԣ Notice there are two paths that represent Ahmed being late. P( L ) = P( C ∩ L ) + P( C′ ∩ L ) = P( C  ) × P( L | C  ) + P( C′  ) × P( L | C′  ) = 0.4 × 0.2 + 0.6 × 0.3 = 0.26 Note that there are two paths giving the probability that B occurs. It is easier to deϐine the meaning of the letters you are using ϐirst and then only use these letters on the tree diagram. The probabilities will then be expressed in the same way as that used in any of the formulae. BOOST G ra d e ⇪⇪⇪⇪