Higher November 2021 Paper 1 Q19
19 Items made at a factory have to pass two checks.
90% pass the first check.
The items that fail are scrapped.
99% of the items that pass the first check pass the second check.
The items that fail are scrapped.
(a) Complete the tree diagram. [2 marks]
(b) An item is chosen at random before the checks.
Work out the probability that the item is scrapped. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| 0.1 on Fail for First check | B1 | oe fraction, decimal or percentage |
| 0.01 on Fail and 0.99 on Pass for Second check | B1 | oe fraction, decimal or percentage |
Additional guidance
Ignore any extra branches drawn
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(0.9 \times\) their 0.01 or 0.009 | M1 | oe eg \(\dfrac{9}{10} \times \dfrac{1}{100} = \dfrac{9}{1000}\) |
| their 0.009 + their 0.1 | M1dep | oe their 0.1 must be \(\gt 0\) and \(\lt 1\) |
| 0.109 | A1ft | oe fraction, decimal or percentage ft their tree diagram if all probabilities are \(\gt 0\) and \(\lt 1\) |
| Alternative method 2 | ||
| \(0.9 \times\) their 0.99 or 0.891 | M1 | oe eg \(\dfrac{9}{10} \times \dfrac{99}{100} = \dfrac{891}{1000}\) |
| \(1 -\) their 0.891 | M1dep | oe |
| 0.109 | A1ft | oe fraction, decimal or percentage ft their tree diagram if all probabilities are \(\gt 0\) and \(\lt 1\) |
Additional guidance
| Answer 0.109% | M2A0 |