Higher June 2019 Paper 1R Q14
14 Each day that Barney goes to college, he either goes by bus or he walks.
The probability that Barney will go to college by bus on any day is 0.3
When Barney goes to college by bus, the probability that he will be late is 0.2
When Barney walks to college, the probability that he will be late is 0.1
(a) Complete the probability tree diagram. (2)
Barney will go to college on 200 days next year.
(b) Work out an estimate for the number of days Barney will be late for college next year. (4)
| Scheme | Marks |
|---|---|
| 0.7, 0.2, 0.8, 0.1, 0.9 | B2 |
| (2) |
Notes
B2: oe, all correct
(B1 for 2 or 3 or 4 correct probabilities)
| Scheme | Marks |
|---|---|
| 0.3 × “0.2” (= 0.06) or 0.7 × “0.1” (= 0.07) oe | M1 |
| 0.3 × “0.2” + 0.7 × “0.1” (= 0.13) oe or “0.06” × 200 (= 12) or “0.07” × 200 (= 14) | M1 |
| “0.13” × 200 oe or “12” + “14” | M1 |
| 26 | A1 |
| (4) | |
| (6 marks) |
Notes
M1: ft from (a) dep on probabilities being between 0 and 1, OR 0.3 × “0.8” (= 0.24) or 0.7 × “0.9” (= 0.63) oe
M1: ft from (a), OR 0.3 × “0.8” + 0.7 × “0.9” (= 0.87) oe or “0.24” × 200 (= 48) or “0.63” × 200 (= 126)
M1: ft from (a), 200 – “0.87” × 200 oe or (1 – “0.87”) × 200 or 200 – “48” – “126”
A1: cao