Higher June 2017 Paper 2 Q19
19. Fifty raffle tickets are sold.
The tickets sold are numbered from 1 to 50.
The raffle tickets are placed in a box for a draw.
One raffle ticket is selected at random and not replaced in the box.
A second ticket is then randomly selected.
(a) Find the probability that one of the tickets drawn is odd and the other is even. [3]
(b) Find the probability that at least one of the tickets drawn is even. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(\frac{25}{50} \times \frac{25}{49}\) \(\left(= \frac{625}{2450} = \frac{25}{98}\right)\) | B1 | |
| \(\frac{25}{50} \times \frac{25}{49} + \frac{25}{50} \times \frac{25}{49}\) | M1 | OR \(2 \times \frac{25}{50} \times \frac{25}{49}\) |
| \(= \frac{1250}{2450}\) \(\left(= \frac{25}{49} = 0.51\ldots\right)\) | A1 | Ignore incorrect cancelling Alternative \(1 \times \frac{25}{49}\) M2 \(\frac{25}{49}\) A1 |
| Scheme | Marks | Comments |
|---|---|---|
| 1 – P(odd, odd) | S1 | FT from (a) P(OE) & P(EO) & P(EE) used OR P(OE) + P(EO) + P(EE) OR FT (a) + P(EE) |
| \(= 1 - \frac{25}{50} \times \frac{24}{49}\) \(\left(= 1 - \frac{24}{98}\right)\) | M1 | \(\frac{25}{50}\times\frac{25}{49}+\frac{25}{50}\times\frac{25}{49}+\frac{25}{50}\times\frac{24}{49}\) OR (a) + \(\frac{25}{50}\times\frac{24}{49}\) |
| \(= \frac{74}{98}\) \(\left(= \frac{37}{49} = 0.755\ldots\right)\) | A1 | CAO. Ignore incorrect cancelling |
| (6) |