Higher November 2020 Paper 2 Q20
20.
(a) On any working day, the probability that Don oversleeps in the morning is 0·3.
When he oversleeps, the probability that he catches his train to work is 0·25.
When Don does not oversleep, he always catches his train.
Work out the probability that, on a randomly chosen working day, Don catches his train to work. [3]
When he oversleeps, the probability that he catches his train to work is 0·25.
When Don does not oversleep, he always catches his train.
Work out the probability that, on a randomly chosen working day, Don catches his train to work. [3]
(b) Don sometimes spends his evenings watching films, playing computer games, or doing both.
On any evening the probability that Don:
On any evening the probability that Don:
- watches films is 0·25,
- plays computer games is 0·45,
- does neither is three times the probability that he does both.
(i) Complete the Venn diagram. [1]
(ii) Work out the probability that, on any randomly chosen evening, Don watches films and plays computer games. [2]
(iii) On the evenings Don watches films, what is the probability that he also plays computer games? [2]
| Scheme | Marks | Comments |
|---|---|---|
| 0.3 × 0.25 + (1 – 0.3) | M2 | M1 for sight of 0.3 × 0.25 |
| 0.775 | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) | ||
Venn diagram correctly completed | B1 | |
| (b)(ii) | ||
| \(x+(0.25-x)+(0.45-x)+3x=1\) | M1 | FT ‘their Venn diagram’ provided of similar difficulty |
| 0.15 | A1 | CAO |
| (b)(iii) | ||
| \(0.15\div0.25\) OR \((F\times0.15)\div(0.25\times F)\) OR \(x\div0.25\) | M1 | FT ‘their 0.15’ |
| 0.6 | A1 | |
| (8) | ||