4MA0 Higher June 2013 Paper 3 Q17
17 Parveen travels to school either by bicycle or by bus.
The probability that, on any day, she will travel by bicycle is 0.7
When she travels by bicycle, the probability that she will be late for school is 0.2
When she travels by bus, the probability that she will be late for school is 0.1
(a) Calculate the probability that, on a randomly chosen day, Parveen will travel by bus and be late for school. (2)
(b) Calculate the probability that, on a randomly chosen day, Parveen will not be late for school. (3)
| Scheme | Marks |
|---|---|
| 0.3 × 0.1 or (1 − 0.7) × 0.1 and no other terms | M1 |
| 0.03 oe | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| 0.7 × 0.8 or 0.7 × (1 − 0.2) or 0.3 × 0.9 or (1 − 0.7) × (1 − 0.1) | M1 |
| 0.7 × 0.8 + 0.3 × 0.9 or 0.7 × (1 − 0.2) + (1 − 0.7) × (1 − 0.1) | M1 |
| 0.83 oe | A1 |
| (3) |
Notes
M1: M1 for “(a)” + 0.7 × 0.2 or
0.3 × 0.1 + 0.7 × 0.2 (=0.17) or
(1 − 0.7) × 0.1 + 0.7 × 0.2
M1: M1 for 1 − (“(a)” + 0.7 × 0.2)
or 1 − “0.17”
(M2 for 1 − “(a)” − 0.7 × 0.2)