Higher June 2022 Paper 2 Q18
18. At a hotel, 70 guests completed a feedback survey.
The survey had 3 statements, A, B and C.
Guests could tick 0, 1, 2 or all 3 of these statements.
The Venn diagram shows the numbers of the 70 guests who ticked each statement.
(a) One of these guests is chosen at random. Find the probability that this guest ticked statement A or statement C but not statement B. [1]
(b) Given that a guest ticked at least one statement, find the probability that this guest ticked statement B. [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{33}{70}\) oe ISW | B1 | Allow B1 for 0.47(142..) or 47(.142..)% |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{31}{64}\) | B2 | Allow B2 for 0.484(375) or 48.4(375)% B1 for sight of \(\dfrac{a}{64}\) with \(a \lt 64\) or \(\dfrac{31}{b}\) with \(31 \lt b \leqslant 70\). ISW for incorrectly simplifying their fraction |
| (3) |