Introduction to Probability Practice Questions

Question 1

3 marks

Do not use a calculator for this question.

Each of the 10 letters of the word

S T A T I S T I C S

is written on a separate card. The 10 cards are placed face down on a table.

Joe takes at random one of the cards.

(a)

Write down the probability that the letter on the card is T.

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(b)

Work out the probability that the letter on the card is not an S.

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(c)

Four arrows, A, B, C and D, are shown on the probability scale below.

Write down the letter of the arrow that best shows the probability that the letter on the card is not an S.

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Question 2

4 marks

Do not use a calculator for this question.

A café sells only tea, coffee, hot chocolate and juice.
The table shows the probabilities that the next customer will buy tea, will buy coffee or will buy hot chocolate.

Drink	tea	coffee	hot chocolate	juice
Probability	0.31	0.24	0.12

(a)

Work out the probability that the next customer will buy juice.

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(b)

Write down the probability that the next customer will not buy coffee.

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(c)

On Saturday, 250 customers buy a drink at the café.

Work out an estimate for the number of these customers who buy hot chocolate.

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Question 3

3 marks

Do not use a calculator for this question.

Amina, Ben and Chloe each spin the same spinner a number of times and record the number of times it lands on red.

	Amina	Ben	Chloe
Number of spins	40	150	60
Number of times it lands on red	14	39	21

(a)

Use all the information in the table to find the best estimate for the probability that the spinner lands on red.

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(b)

Whose results on their own would give the best estimate for the probability that the spinner lands on red?
Give a reason for your answer.

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Question 4

5 marks

Do not use a calculator for this question.

Spinner A has three equal sections numbered 1, 2 and 3.
Spinner B has four equal sections numbered 1, 2, 3 and 4.
Both spinners are fair.

Maya spins each spinner once and adds the two numbers she gets to give her total.

(a)

Complete the sample space diagram to show all the possible totals.

$+$	1	2	3	4
1	2	3	4	5
2	3
3				7

(The numbers along the top are the score on spinner B. The numbers down the side are the score on spinner A.)

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(b)

Work out the probability that Maya's total is 5.

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(c)

Work out the probability that Maya's total is an odd number.

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Question 0

5 marks

Do not use a calculator for this question.

A bowl contains only red grapes, green grapes and purple grapes.
There are 3 times as many green grapes as red grapes.
The number of purple grapes is half the number of green grapes.

(a)

Rachel takes at random a grape from the bowl.

Work out the probability that she takes a purple grape.

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(b)

There are 12 purple grapes in the bowl.

Work out the total number of grapes in the bowl.

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Question 0

6 marks

Do not use a calculator for this question.

Owen rolls a fair ordinary six-sided dice twice.
He works out the difference between his two scores by subtracting the smaller score from the larger score.
(If both scores are the same, the difference is 0.)

(a)

Complete the sample space diagram to show all the possible differences.

Difference	1	2	3	4	5	6
1	0	1	2	3	4	5
2	1
3	2
4	3
5	4
6	5

(The numbers along the top are the first score. The numbers down the side are the second score.)

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(b)

Work out the probability that the difference is 1.

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(c)

Work out the probability that the difference is at least 4.

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Question 0

3 marks

Do not use a calculator for this question.

A spinner has four equal sections, labelled A, B, C and D.
Lena spins the spinner 120 times. Her results are shown in the table.

Section	A	B	C	D
Frequency	18	44	30	28

(a)

If the spinner were fair, how many times would you expect it to land on section A in 120 spins?

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(b)

Use Lena's results to estimate the probability that the spinner lands on section B.

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(c)

Lena says the spinner is biased.

Do you agree with Lena? You must give a reason for your answer based on the results in the table.

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Question 0

4 marks

Do not use a calculator for this question.

A box contains only milk chocolates, dark chocolates, white chocolates and caramel chocolates.
Harvey is going to take at random one chocolate from the box.
The table shows the probability that the chocolate will be dark and the probability that it will be caramel.

Type	milk	dark	white	caramel
Probability		0.4		0.2

There are 24 dark chocolates in the box.
The probability that Harvey takes a milk chocolate is 3 times the probability that he takes a white chocolate.

Work out the number of milk chocolates in the box.

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Question 0

5 marks

Do not use a calculator for this question.

A bag contains exactly 240 beads.
Each bead is red or blue or green.
The number of red beads is 90, correct to the nearest 10.
The number of blue beads is 60, correct to the nearest 10.
A bead is taken at random from the bag.

(a)

Work out the upper bound of the probability that the bead is red.

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(b)

Work out the lower bound of the probability that the bead is green.

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Question 0

8 marks

Do not use a calculator for this question.

In a game, two fair spinners are used.
Each spinner has four equal sections numbered 1, 2, 3 and 4.
Both spinners are spun once and the two numbers they land on are multiplied together to give the score.

(a)

Complete the sample space diagram to show all the possible scores.

$\times$	1	2	3	4
1	1	2	3	4
2	2	4
3	3
4	4			16

(The numbers along the top are the score on the first spinner. The numbers down the side are the score on the second spinner.)

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(b)

Work out the probability that the score is a multiple of 3.

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(c)

Ali wins the game if the score is greater than 8.
Ben wins the game if the score is 8 or less.

Is this game fair? You must show your working.

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(d)

Ali and Ben play the game 60 times.

Work out how many more times Ben would be expected to win than Ali.

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Number

Algebra

Ratio, Proportion & Rates of Change

Geometry & Measures

Probability

Statistics

Question 1

Question 2

Question 3

Question 4

Question 0

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Question 0

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