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Date	May 2019	Marks available	2	Reference code	19M.1.SL.TZ1.T_12
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 1
Command term	Find	Question number	T_12	Adapted from	N/A

Question

The diagram shows a circular horizontal board divided into six equal sectors. The sectors are labelled white (W), yellow (Y) and blue (B).

A pointer is pinned to the centre of the board. The pointer is to be spun and when it stops the colour of the sector on which the pointer stops is recorded. The pointer is equally likely to stop on any of the six sectors.

Eva will spin the pointer twice. The following tree diagram shows all the possible outcomes.

Find the probability that both spins are yellow.

[2]

a.

Find the probability that at least one of the spins is yellow.

[3]

b.

Write down the probability that the second spin is yellow, given that the first spin is blue.

[1]

c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$\frac{1}{3} \times \frac{1}{3}$ OR ${\left( {\frac{1}{3}} \right)^2}$ (M1)

Note: Award (M1) for multiplying correct probabilities.

$\frac{1}{9}$ (0.111, 0.111111…, 11.1%) (A1) (C2)

[2 marks]

a.

$\left( {\frac{1}{2} \times \frac{1}{3}} \right) + \left( {\frac{1}{6} \times \frac{1}{3}} \right) + \frac{1}{3}$ (M1)(M1)

Note: Award (M1) for $\left( {\frac{1}{2} \times \frac{1}{3}} \right)$ and $\left( {\frac{1}{6} \times \frac{1}{3}} \right)$ or equivalent, and (M1) for $\frac{1}{3}$ and adding only the three correct probabilities.

OR

$1 - {\left( {\frac{2}{3}} \right)^2}$ (M1)(M1)

Note: Award (M1) for ${\frac{2}{3}}$ seen and (M1) for subtracting ${\left( {\frac{2}{3}} \right)^2}$ from 1. This may be shown in a tree diagram with “yellow” and “not yellow” branches.

$\frac{5}{9}$ (0.556, 0.555555…, 55.6%) (A1)(ft) (C3)

Note: Follow through marks may be awarded if their answer to part (a) is used in a correct calculation.

[3 marks]

b.

$\frac{1}{3}$ (0.333, 0.333333…, 33.3%) (A1) (C1)

[1 mark]

c.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

Syllabus sections

Topic 5—Calculus » SL 5.5—Integration introduction, areas between curve and x axis

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