Higher June 2023 Paper 2 Q9
9. A factory makes loaves of bread which are wrapped in packaging.
Independently, for any loaf wrapped in packaging, chosen at random:
- The probability that there is a fault with the bread is 0·02.
- The probability that there is a fault with the packaging is 0·01.
(a) Complete the tree diagram to show this information. [2]
(b) A loaf wrapped in packaging is chosen at random.
(i) Calculate the probability that neither the bread nor the packaging has a fault. [2]
(ii) Calculate the probability that either the bread or the packaging has a fault but they do not both have a fault. [3]
| Scheme | Marks | Comments |
|---|---|---|
Correctly completes the tree diagram | B1 B1 | 0.98 correctly placed 0.01 and 0.99 correctly placed on both pairs of branches |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) \(0.98 \times 0.99\) | M1 | FT ‘their 0.98 and 0.99’ from their tree diagram provided they are less than 1 |
| 0.9702 or \(\dfrac{4851}{5000}\) oe | A1 | FT Allow 0.97 from correct working (not if unsupported) |
| (b)(ii) \((0.02 \times 0.99) + (0.98 \times 0.01)\) | M2 | For M1 or M2, FT their probabilities from their tree provided they are less than 1 M1 for either \((0.02 \times 0.99)\) or \((0.98 \times 0.01)\) |
| 0.0296 or \(\dfrac{37}{1250}\) oe | A1 | FT Allow 0.03 from correct working (not if unsupported) |
| (7) |