Sec 2 G2 Maths Probability worksheet with answers

A free Sec 2 G2 Maths worksheet on probability: 7 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 2 G2 Maths worksheet: Probability

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

A bag contains

6

red balls and some blue balls. The probability of taking a red ball is

\dfrac{1}{3}

. Find the number of blue balls in the bag.

Answer[2]

	Members	Non-members	Total
Adults	18	7	25
Children	11	14	25
Total	29	21	50

The two-way table shows the visitors to a museum one morning. A visitor is chosen at random. Find the probability that the visitor is not a member.

Answer[2]

(a)Cards numbered

1

24

are shuffled and one is drawn at random. Find the probability that the number is a factor of 24.

Answer (a)[2]

(b)Cards numbered

1

15

are shuffled and one is drawn at random. Find the probability that the number is a prime number.

Answer (b)[2]

Section B

(a)A bag contains

3

red,

9

blue and

6

green balls. A ball is taken at random. Find the probability that it is red.

Answer (a)[2]

(b)A bag contains

5

red,

3

blue and

4

green balls. A ball is taken at random. Find the probability that it is red.

Answer (b)[2]

(a)Cards numbered

1

20

are shuffled and one is drawn at random. Find the probability that the number is an even number.

Answer (a)[2]

(b)(i)A bag contains

5

red,

3

blue and

4

green balls. A ball is taken at random. Find the probability that it is blue.

Answer (b)(i)[2]

(b)(ii)A bag contains

6

red,

2

blue and

4

green balls. A ball is taken at random. Find the probability that it is red.

Answer (b)(ii)[2]

(a)Cards numbered

1

12

are shuffled and one is drawn at random. Find the probability that the number is an even number.

Answer (a)[2]

(b)(i)Cards numbered

1

20

are shuffled and one is drawn at random. Find the probability that the number is a perfect square.

Answer (b)(i)[2]

(b)(ii)Cards numbered

1

15

are shuffled and one is drawn at random. Find the probability that the number is a prime number.

Answer (b)(ii)[2]

(a)A bag contains

6

red,

2

blue and

4

green balls. A ball is taken at random. Find the probability that it is red or blue.

Answer (a)[2]

(b)(i)A bag contains

6

red balls and some blue balls. The probability of taking a red ball is

\dfrac{1}{2}

. Find the number of blue balls in the bag.

Answer (b)(i)[2]

(b)(ii)A bag contains

3

red balls and some blue balls. The probability of taking a red ball is

\dfrac{1}{4}

. Find the number of blue balls in the bag.

Answer (b)(ii)[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

\text{Blue} = 12

[2]

\dfrac{6}{n} = \dfrac{1}{3}

\mathstrut n = 6 \times \dfrac{3}{1}

n = 18

\mathstrut \text{Blue} = 18 - 6

\text{Blue} = 12

Question 2

Answer:

P = \dfrac{21}{50}

[2]

7 + 14 = 21

Grand total

= 50

P = \dfrac{21}{50}

Question 3

(a)Answer:

P = \dfrac{1}{3}

[2]

1, 2, 3, 4, 6, 8, 12, 24

That is

8

numbers out of

24

\mathstrut P = \dfrac{8}{24}

P = \dfrac{1}{3}

(b)Answer:

P = \dfrac{2}{5}

[2]

2, 3, 5, 7, 11, 13

That is

6

numbers out of

15

\mathstrut P = \dfrac{6}{15}

P = \dfrac{2}{5}

Question 4

(a)Answer:

P(\text{red}) = \dfrac{1}{6}

[2]

\mathstrut \text{Total} = 3 + 9 + 6

\text{Total} = 18

\mathstrut P(\text{red}) = \dfrac{3}{18}

P(\text{red}) = \dfrac{1}{6}

(b)Answer:

\mathstrut P(\text{red}) = \dfrac{5}{12}

[2]

\mathstrut \text{Total} = 5 + 3 + 4

\text{Total} = 12

\mathstrut P(\text{red}) = \dfrac{5}{12}

Question 5

(a)Answer:

P = \dfrac{1}{2}

[2]

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

That is

10

numbers out of

20

\mathstrut P = \dfrac{10}{20}

P = \dfrac{1}{2}

(b)(i)Answer:

P(\text{blue}) = \dfrac{1}{4}

[2]

\mathstrut \text{Total} = 5 + 3 + 4

\text{Total} = 12

\mathstrut P(\text{blue}) = \dfrac{3}{12}

P(\text{blue}) = \dfrac{1}{4}

(b)(ii)Answer:

P(\text{red}) = \dfrac{1}{2}

[2]

\mathstrut \text{Total} = 6 + 2 + 4

\text{Total} = 12

\mathstrut P(\text{red}) = \dfrac{6}{12}

P(\text{red}) = \dfrac{1}{2}

Question 6

(a)Answer:

P = \dfrac{1}{2}

[2]

2, 4, 6, 8, 10, 12

That is

6

numbers out of

12

\mathstrut P = \dfrac{6}{12}

P = \dfrac{1}{2}

(b)(i)Answer:

P = \dfrac{1}{5}

[2]

1, 4, 9, 16

That is

4

numbers out of

20

\mathstrut P = \dfrac{4}{20}

P = \dfrac{1}{5}

(b)(ii)Answer:

P = \dfrac{2}{5}

[2]

2, 3, 5, 7, 11, 13

That is

6

numbers out of

15

\mathstrut P = \dfrac{6}{15}

P = \dfrac{2}{5}

Question 7

(a)Answer:

P = \dfrac{2}{3}

[2]

\mathstrut \text{Favourable} = 6 + 2

\text{Favourable} = 8

\mathstrut P = \dfrac{8}{12}

P = \dfrac{2}{3}

(b)(i)Answer:

\text{Blue} = 6

[2]

\dfrac{6}{n} = \dfrac{1}{2}

\mathstrut n = 6 \times \dfrac{2}{1}

n = 12

\mathstrut \text{Blue} = 12 - 6

\text{Blue} = 6

(b)(ii)Answer:

\text{Blue} = 9

[2]

\dfrac{3}{n} = \dfrac{1}{4}

\mathstrut n = 3 \times \dfrac{4}{1}

n = 12

\mathstrut \text{Blue} = 12 - 3

\text{Blue} = 9

Sec 2 G2 Maths Probability worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Members

Non-members

Total

Adults

Children

Total

Answers and worked solutions

Question 1

Answer:

\text{Blue} = 12

[2]

\dfrac{6}{n} = \dfrac{1}{3}

\mathstrut n = 6 \times \dfrac{3}{1}

n = 18

\mathstrut \text{Blue} = 18 - 6

\text{Blue} = 12

Question 2

Answer:

P = \dfrac{21}{50}

[2]

7 + 14 = 21

Grand total

= 50

P = \dfrac{21}{50}

Question 3

(a)Answer:

P = \dfrac{1}{3}

[2]

1, 2, 3, 4, 6, 8, 12, 24

That is

8

numbers out of

24

\mathstrut P = \dfrac{8}{24}

P = \dfrac{1}{3}

(b)Answer:

P = \dfrac{2}{5}

[2]

2, 3, 5, 7, 11, 13

That is

6

numbers out of

15

\mathstrut P = \dfrac{6}{15}

P = \dfrac{2}{5}

Question 4

(a)Answer:

P(\text{red}) = \dfrac{1}{6}

[2]

\mathstrut \text{Total} = 3 + 9 + 6

\text{Total} = 18

\mathstrut P(\text{red}) = \dfrac{3}{18}

P(\text{red}) = \dfrac{1}{6}

(b)Answer:

\mathstrut P(\text{red}) = \dfrac{5}{12}

[2]

\mathstrut \text{Total} = 5 + 3 + 4

\text{Total} = 12

\mathstrut P(\text{red}) = \dfrac{5}{12}

Question 5

(a)Answer:

P = \dfrac{1}{2}

[2]

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

That is

10

numbers out of

20

\mathstrut P = \dfrac{10}{20}

P = \dfrac{1}{2}

(b)(i)Answer:

P(\text{blue}) = \dfrac{1}{4}

[2]

\mathstrut \text{Total} = 5 + 3 + 4

\text{Total} = 12

\mathstrut P(\text{blue}) = \dfrac{3}{12}

P(\text{blue}) = \dfrac{1}{4}

(b)(ii)Answer:

P(\text{red}) = \dfrac{1}{2}

[2]

\mathstrut \text{Total} = 6 + 2 + 4

\text{Total} = 12

\mathstrut P(\text{red}) = \dfrac{6}{12}

P(\text{red}) = \dfrac{1}{2}

Question 6

(a)Answer:

P = \dfrac{1}{2}

[2]

2, 4, 6, 8, 10, 12

That is

6

numbers out of

12

\mathstrut P = \dfrac{6}{12}

P = \dfrac{1}{2}

(b)(i)Answer:

P = \dfrac{1}{5}

[2]

1, 4, 9, 16

That is

4

numbers out of

20

\mathstrut P = \dfrac{4}{20}

P = \dfrac{1}{5}

(b)(ii)Answer:

P = \dfrac{2}{5}

[2]

2, 3, 5, 7, 11, 13

That is

6

numbers out of

15

\mathstrut P = \dfrac{6}{15}

P = \dfrac{2}{5}

Question 7

(a)Answer:

P = \dfrac{2}{3}

[2]

\mathstrut \text{Favourable} = 6 + 2

\text{Favourable} = 8

\mathstrut P = \dfrac{8}{12}

P = \dfrac{2}{3}

(b)(i)Answer:

\text{Blue} = 6

[2]

\dfrac{6}{n} = \dfrac{1}{2}

\mathstrut n = 6 \times \dfrac{2}{1}

n = 12

\mathstrut \text{Blue} = 12 - 6

\text{Blue} = 6

(b)(ii)Answer:

\text{Blue} = 9

[2]

\dfrac{3}{n} = \dfrac{1}{4}

\mathstrut n = 3 \times \dfrac{4}{1}

n = 12

\mathstrut \text{Blue} = 12 - 3

\text{Blue} = 9