4400 Higher November 2005 Paper 3 Q19
19 The probability that Gill will walk to school on Monday is \(\frac{3}{5}\).
If Gill walks to school on Monday, the probability that she will walk to school on Tuesday is \(\frac{1}{6}\).
If she does not walk to school on Monday, the probability that she will walk to school on Tuesday is \(\frac{7}{10}\).
(a) Calculate the probability that she walks to school on Monday but not on Tuesday. (2)
(b) Calculate the probability that she walks to school on at least one of the two days. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{5} \times \dfrac{5}{6}\) | M1 |
| \(\dfrac{1}{2}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{5} + \dfrac{2}{5} \times \dfrac{7}{10}\) or \(\dfrac{3}{5} \times \dfrac{5}{6} + \dfrac{2}{5} \times \dfrac{7}{10} + \dfrac{3}{5} \times \dfrac{1}{6}\) or \(\dfrac{1}{2} + \dfrac{2}{5} \times \dfrac{7}{10} + \dfrac{3}{5} \times \dfrac{1}{6}\) or \(1 - \dfrac{2}{5} \times \dfrac{3}{10}\) | M1 M1 |
| \(\dfrac{44}{50}\) or \(\dfrac{22}{25}\) | A1 |
| (3) | |
| (5 marks) |
Notes
M1: for one correct product or term
M1: for complete correct expression
SC if no marks in either part M1 for correct tree diagram