Foundation November 2018 Unit 1 Q18
18. A box contains five identical balls numbered 1 to 5 respectively.
One ball is chosen at random from the box.
Its number is recorded and the ball is replaced in the box.
This process was carried out 75 times in total.
How many times would you expect an even-numbered ball to have been chosen?
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| Recognising that each number has a one in five chance of being chosen. | B1 | May be expressed in words e.g. ‘ 2 (even) numbers out of 5’, ‘ each number has a one in 5 chance’ OR as a probability e.g. sight of 2/5, ‘(probability of choosing each ball =) 1/5’ B0 if no reference to ‘out of 5’ or ‘in 5’. |
| (Expected number of even numbers =) \(\dfrac{2}{5} \times 75\) | M1 | M1 for 1/5 × 75 × 2 or equivalent. M1 implies the B1. |
| = 30 | A1 | 30/75 gains B1 M1 A0 if 30 on its own is not shown. |