GCSE Maths · Higher · Chapter 13: Exploring and applying probability · Lesson 2

Outcomes, two-way tables and Venn diagrams

Grades 4–7About 45 minutesNo calculator34 marks

Hints online, answers free with an account:
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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
A bag holds 6 red and 6 blue counters. Find P(red).
[1 mark]
Answer
A2
Last lesson
A spinner lands on red 12 times in 50 spins. Find the relative frequency of red.
[1 mark]
Answer
A3
From chapter 12
Lengths are multiplied by 5. What is area multiplied by?
[1 mark]
Answer
A4
From chapter 3
A line of best fit is $y = 3 x + 13$ . Estimate $y$ when $x = 9$ .
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

In a group of 50 people, 31 have a laptop, 24 have a tablet and 13 have both. How many have neither?

Hint Put the 13 in the overlap of a Venn diagram first, then fill in the rest.

B1
Of 64 students, 37 study art, 29 study music and 11 study both. Work out P(a student chosen at random studies neither).
[3 marks]
Answer

Example 2

$P (A) = 0.4$ , $P (B) = 0.35$ and $P (A and B) = 0.1$ . Work out $P (A or B)$ .

Hint Adding

P (A)

and

P (B)

counts the overlap twice, so take it away once.

B2
$P (A) = 0.7$ , $P (A or B) = 0.85$ and $P (A and B) = 0.25$ . Work out $P (B)$ .
[2 marks]
Answer

Grades 5–6

C1
A bag holds red, white and blue counters only. $P (red) = 0.2$ and $P (white)$ is three times $P (blue)$ . Work out $P (blue)$ .
[2 marks]
Answer
C2
$P (A) = 0.55$ , $P (B) = 0.3$ and $P (A and B) = 0.15$ . Work out $P (neither A nor B)$ .
[2 marks]
Answer

C3
A card is taken from cards numbered 1 to 20. $A$ : a multiple of 6. $B$ : a prime number. Are $A$ and $B$ mutually exclusive? Give a reason.
[2 marks]
C4
The Venn diagram shows numbers of people. One is chosen at random. Work out P(exactly one of $A$ and $B$ ).
[2 marks]
Answer
C5
$ξ$ is the whole numbers from 1 to 24. $A$ is the factors of 24 and $B$ is the even numbers. A number is chosen at random from $ξ$ . Work out $P (A \cup B)$ .
[2 marks]
Answer
C6
The Venn diagram shows probabilities. Work out $P (B)$ .
[2 marks]
Answer

Grades 6–7

D1
Ravi says, " $P (rain) = 0.6$ and $P (wind) = 0.5$ , so $P (rain or wind) = 0.6 + 0.5 = 1.1$ ."
$P (rain and wind) = 0.35$ . Explain why Ravi is wrong, and work out $P (rain or wind)$ .
[3 marks]
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use the fact that the probabilities of all the outcomes add to 1.
I can read a two-way table or Venn diagram and use the addition rule.

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