Sec 2 Maths Probability worksheet with answers

A free Sec 2 Maths worksheet on probability: 6 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 Maths worksheet: Probability

Total: 30 marksSuggested time: 45 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)A bag contains

6

red,

2

blue and

4

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

Answer (a)[2]

(b)Cards numbered

1

20

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

Answer (b)[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)A bag contains

5

red balls and

7

blue balls.

x

more blue balls are put into the bag. A ball is then taken at random. The probability that it is red is

\dfrac{5}{17}

. Find the value of

x

Answer (b)[3]

Section B

	Members	Non-members	Total
Adults	7	15	22
Children	10	8	18
Total	17	23	40

(a)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 a member.

Answer (a)[2]

(b)Cards numbered

1

12

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

Answer (b)[2]

(a)A bag contains

7

red,

5

blue,

3

green and

5

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

Answer (a)[2]

(b)A bag contains

7

red balls and

5

blue balls.

x

more red balls are put into the bag. A ball is then taken at random. The probability that it is red is

\dfrac{13}{18}

. Find the value of

x

Answer (b)[3]

(a)A bag contains

6

red balls and

10

blue balls.

x

more red balls are put into the bag. A ball is then taken at random. The probability that it is red is

\dfrac{1}{2}

. Find the value of

x

Answer (a)[2]

(b)(i)A bag contains

3

red,

5

blue and

7

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

Answer (b)(i)[2]

(b)(ii)A bag contains

5

red balls and

10

blue balls.

x

more blue balls are put into the bag. A ball is then taken at random. The probability that it is red is

\dfrac{1}{4}

. Find the value of

x

Answer (b)(ii)[2]

(a)Cards numbered

1

24

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

15

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

Answer (b)(i)[2]

(b)(ii)A bag contains

5

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 (b)(ii)[2]

END OF PAPER

Answers and worked solutions

Question 1

(a)Answer:

P(\text{green}) = \dfrac{1}{3}

[2]

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

\text{Total} = 12

\mathstrut P(\text{green}) = \dfrac{4}{12}

P(\text{green}) = \dfrac{1}{3}

(b)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}

Question 2

(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)Answer:

x = 5

[3]

Red balls:

5

; all the balls:

12 + x

\dfrac{5}{12 + x} = \dfrac{5}{17}

17(5) = 5(12 + x)

85 = 60 + 5x

5x = 25

x = 5

Question 3

(a)Answer:

P = \dfrac{17}{40}

[2]

7 + 10 = 17

Grand total

= 40

P = \dfrac{17}{40}

(b)Answer:

P = \dfrac{5}{12}

[2]

2, 3, 5, 7, 11

That is

5

numbers out of

12

P = \dfrac{5}{12}

Question 4

(a)Answer:

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

[2]

\mathstrut \text{Total} = 7 + 5 + 3 + 5

\text{Total} = 20

\mathstrut P(\text{blue}) = \dfrac{5}{20}

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

(b)Answer:

x = 6

[3]

Red balls:

7 + x

; all the balls:

12 + x

\dfrac{7 + x}{12 + x} = \dfrac{13}{18}

18(7 + x) = 13(12 + x)

126 + 18x = 156 + 13x

5x = 30

x = 6

Question 5

(a)Answer:

x = 4

[2]

Red balls:

6 + x

; all the balls:

16 + x

\dfrac{6 + x}{16 + x} = \dfrac{1}{2}

2(6 + x) = 1(16 + x)

12 + 2x = 16 + x

x = 4

(b)(i)Answer:

P(\text{blue}) = \dfrac{1}{3}

[2]

\mathstrut \text{Total} = 3 + 5 + 7

\text{Total} = 15

\mathstrut P(\text{blue}) = \dfrac{5}{15}

P(\text{blue}) = \dfrac{1}{3}

(b)(ii)Answer:

x = 5

[2]

Red balls:

5

; all the balls:

15 + x

\dfrac{5}{15 + x} = \dfrac{1}{4}

4(5) = 1(15 + x)

20 = 15 + x

x = 5

Question 6

(a)Answer:

P = \dfrac{1}{2}

[2]

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

That is

12

numbers out of

24

\mathstrut P = \dfrac{12}{24}

P = \dfrac{1}{2}

(b)(i)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}

(b)(ii)Answer:

\text{Blue} = 10

[2]

\dfrac{5}{n} = \dfrac{1}{3}

\mathstrut n = 5 \times \dfrac{3}{1}

n = 15

\mathstrut \text{Blue} = 15 - 5

\text{Blue} = 10

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Sec 2 Maths Probability worksheet with answers

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

Need the formulas first? Read the Probability notes. Or practise it online with step-by-step help when you get one wrong.

Section B

	Members	Non-members	Total
Adults	7	15	22
Children	10	8	18
Total	17	23	40

(a)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 a member.

Answer (a)[2]

(b)Cards numbered

1

12

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

Answer (b)[2]

Answers and worked solutions

Question 1

(a)Answer:

P(\text{green}) = \dfrac{1}{3}

[2]

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

\text{Total} = 12

\mathstrut P(\text{green}) = \dfrac{4}{12}

P(\text{green}) = \dfrac{1}{3}

(b)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}

Question 2

(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)Answer:

x = 5

[3]

Red balls:

5

; all the balls:

12 + x

\dfrac{5}{12 + x} = \dfrac{5}{17}

17(5) = 5(12 + x)

85 = 60 + 5x

5x = 25

x = 5

Question 3

(a)Answer:

P = \dfrac{17}{40}

[2]

7 + 10 = 17

Grand total

= 40

P = \dfrac{17}{40}

(b)Answer:

P = \dfrac{5}{12}

[2]

2, 3, 5, 7, 11

That is

5

numbers out of

12

P = \dfrac{5}{12}

Question 4

(a)Answer:

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

[2]

\mathstrut \text{Total} = 7 + 5 + 3 + 5

\text{Total} = 20

\mathstrut P(\text{blue}) = \dfrac{5}{20}

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

(b)Answer:

x = 6

[3]

Red balls:

7 + x

; all the balls:

12 + x

\dfrac{7 + x}{12 + x} = \dfrac{13}{18}

18(7 + x) = 13(12 + x)

126 + 18x = 156 + 13x

5x = 30

x = 6

Question 5

(a)Answer:

x = 4

[2]

Red balls:

6 + x

; all the balls:

16 + x

\dfrac{6 + x}{16 + x} = \dfrac{1}{2}

2(6 + x) = 1(16 + x)

12 + 2x = 16 + x

x = 4

(b)(i)Answer:

P(\text{blue}) = \dfrac{1}{3}

[2]

\mathstrut \text{Total} = 3 + 5 + 7

\text{Total} = 15

\mathstrut P(\text{blue}) = \dfrac{5}{15}

P(\text{blue}) = \dfrac{1}{3}

(b)(ii)Answer:

x = 5

[2]

Red balls:

5

; all the balls:

15 + x

\dfrac{5}{15 + x} = \dfrac{1}{4}

4(5) = 1(15 + x)

20 = 15 + x

x = 5

Question 6

(a)Answer:

P = \dfrac{1}{2}

[2]

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

That is

12

numbers out of

24

\mathstrut P = \dfrac{12}{24}

P = \dfrac{1}{2}

(b)(i)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}

(b)(ii)Answer:

\text{Blue} = 10

[2]

\dfrac{5}{n} = \dfrac{1}{3}

\mathstrut n = 5 \times \dfrac{3}{1}

n = 15

\mathstrut \text{Blue} = 15 - 5

\text{Blue} = 10