Higher November 2021 Paper 2 Q21
21. The following probabilities are given for events \(A\) and \(B\).
\[P(A) = 0{\cdot}3 \qquad P(B) = 0{\cdot}6 \qquad P(A \cup B) = 0{\cdot}72\](a) By drawing a Venn diagram or otherwise, find the probability that \(A\) occurs or \(B\) occurs but they do not both occur. [3]
(b) Find \(P(A' \cap B')\). [2]
| Scheme | Marks | Comments |
|---|---|---|
Correctly completed Venn diagram e.g. or 0.3 + 0.6 – 2(0.18) or equivalent | B2 | B1 for sight of a correct method to find the intersection e.g. 0.3 + 0.6 – 0.72 or \(0.3 - x + x + 0.6 - x = 0.72\) or sight of 0.18 |
| 0.54 | B1 | FT ‘their 0.12 + 0.42’ or 0.3 + 0.6 – 2(‘their 0.18’); correct answer implies B2 B1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(1 - P(A \cup B)\) or equivalent or correct region on Venn diagram indicated | S1 | |
| 0.28 | B1 | implies S1 FT ‘their Venn diagram’ |
| (5) |