4MA0 Higher June 2017 Paper 4 Q5
5 Each time Astrid plays a game of chess against her computer, she will win or draw or lose.
For each game of chess
the probability that she will win is 0.3
the probability that she will lose is three times the probability that she will draw.
On Monday, Astrid is going to play 20 games of chess against her computer.
(a) Work out an estimate for the number of games of chess Astrid wins on Monday. (2)
On Tuesday, Astrid plays a game of chess against her computer.
(b) Work out the probability that she will lose. (3)
| Scheme | Marks |
|---|---|
| 20 × 0.3 | M1 |
| 6 | A1 |
| (2) |
Notes
M1: Or for an answer of \(\dfrac{6}{20}\)
A1: condone ‘6 out of 20’
| Scheme | Marks |
|---|---|
| \(0.3 + x + 3x = 1\) | M1 |
| (1 – 0.3) ÷ 4 or 0.175 or (1 – 0.3) × 0.75 | M1 |
| 0.525 | A1 |
| (3) | |
| (5 marks) |
Notes
M1: oe, e.g. \(4x = 0.7\)
M1: complete method to find \(x\) or \(3x\)
A1: oe, e.g. \(\dfrac{21}{40}\), 52.5%
(accept 0.53 from correct working)
M1 for (20 – “6”) ÷ 4 (=3.5)
M1 for \(\dfrac{3 \times \text{“}3.5\text{”}}{20}\)
A1 for 0.525 oe