Probability: The Complete Grade 8–9 Guide — Worksheet & Memo

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Grade 8–9 · Probability

Probability: The Complete Grade 8–9 Guide

MARKING GUIDELINE

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 31

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
A fair die is rolled once. P(rolling a 4) is …
(1)
A)14
B)16✓
C)46
D)12
Answer: B — One favourable outcome out of six equally likely ones.
- A — the 4 on the die is not the number of outcomes
- C — that would be P(rolling 4 or less)
- D — that is P(an even number)
1.2
A fair die is rolled once. P(an EVEN number) is …
(1)
A)16
B)12✓
C)13
D)23
Answer: B — Three of the six outcomes (2, 4, 6) are even.
- A — that is the chance of ONE particular number
- C — that is P(a multiple of 3)
- D — that is P(not a multiple of 3)
1.3
The probability of an event that is CERTAIN is …
(1)
A)0
B)1✓
C)0,5
D)100
Answer: B — Probabilities run from 0 (impossible) to 1 (certain).
- A — that is IMPOSSIBLE
- C — that is an even chance
- D — that would be 100 PER CENT, not a probability
1.4
If P(A) = 0,3, then P(NOT A) is …
(1)
A)0,3
B)0,7✓
C)−0,3
D)1,3
Answer: B — Complementary events add up to 1.
- A — that is P(A) itself
- C — a probability cannot be negative
- D — a probability cannot exceed 1
1.5
A bag has 4 red and 6 blue balls. P(red) is …
(1)
A)46
B)25✓
C)14
D)610
Answer: B — 4 out of 10, which simplifies to 2/5.
- A — compared red with blue instead of with the total
- C — used the number of red as the denominator
- D — that is P(blue)
1.6
Two coins are tossed. The number of possible outcomes is …
(1)
A)2
B)4✓
C)3
D)8
Answer: B — HH, HT, TH, TT.
- A — that is the outcomes for ONE coin
- C — HT and TH are different outcomes
- D — that is for three coins
1.7
Two coins are tossed. P(two heads) is …
(1)
A)12
B)14✓
C)13
D)24
Answer: B — One favourable outcome (HH) out of four.
- A — that is P(one particular coin showing heads)
- C — there are four outcomes, not three
- D — that is P(exactly one head)
1.8
Relative frequency differs from theoretical probability because it is based on …
(1)
A)what SHOULD happen
B)what ACTUALLY happened in trials✓
C)the number of outcomes only
D)guesswork
Answer: B — It is the observed count divided by the number of trials.
- A — that is theoretical probability
- C — the trials are what matter
- D — it is measured, not guessed
1.9
A coin is tossed 100 times and lands on heads 46 times. The relative frequency of heads is …
(1)
A)0,5
B)0,46✓
C)46
D)54
Answer: B — 46 ÷ 100.
- A — that is the THEORETICAL probability
- C — that is the count, not a probability
- D — that is the number of tails
1.10
Two events that CANNOT happen at the same time are …
(1)
A)complementary
B)mutually exclusive✓
C)independent
D)certain
Answer: B — Mutually exclusive events have no outcome in common.
- A — complementary events are mutually exclusive AND cover everything
- C — independent events can happen together
- D — certain events always happen

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[10 MARKS]

A bag contains 5 red marbles, 7 blue marbles and 8 green marbles. One marble is drawn at random.

2.1
Write down P(red) as a fraction in its simplest form AND as a percentage.
(3)
Total = 5 + 7 + 8 = 20 (1)
P(red) = 520 = 14 (1)
= 25% (1)
2.2
Determine P(not green). Show your working.
(3)
Not green = 5 + 7 = 12 (1)
P(not green) = 1220 (1)
= 35 (1)
2.3
One green marble is drawn and NOT replaced. Determine the probability that the next marble drawn is also green.
(4)
Green left = 8 − 1 = 7 (1)
Marbles left = 20 − 1 = 19 (1)
P(green) = 719 (2)

Question 3

[11 MARKS]

Answer the following.

3.1
Two coins are tossed at the same time. Write down the sample space, and hence determine the probability of getting exactly ONE head.
(4)
S = {HH ; HT ; TH ; TT} (2)
Exactly one head: HT and TH (1)
P = 24 = 12 (1)
3.2
An ordinary die is rolled once. Determine the probability of rolling a prime number.
(3)
The primes on a die are 2 ; 3 ; 5 (2)
P(prime) = 36 = 12 (1)
3.3
A coin is tossed 200 times and lands on heads 118 times. Calculate the relative frequency of heads, and explain why it is not exactly equal to the theoretical probability.
(4)
Relative frequency = 118200 = 0,59 (2)
The theoretical probability is 0,5 (1)
Chance causes variation in a real experiment; the more tosses, the closer the two usually become (1)

TOTAL: 31 marks

This question paper consists of 3 questions.