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12.03 Calculating probability

Worksheet
Probability calculations
1

State the probability of landing on a head when flipping a coin.

2

Amy picks a whole number between 4 and 8 inclusive.

a

List the sample space.

b

Find the probability that Amy picked the number 5.

c

Find the probability that Amy picked the number 1.

d

Find the probability that Amy picked an even number.

3

A number is randomly selected from the following list:

\left\{1,\, 3,\, 3,\, 6,\, 6,\, 6,\, 8,\, 8,\, 8,\, 8,\, 10,\, 10,\, 10,\, 10,\, 10\right\}

a

Find the probability of selecting the following numbers:

i
1
ii
3
iii
8
b

State the number most likely to be selected.

4

A number is randomly selected from the following list:

\left\{3,\, 5,\, 5,\, 6,\, 6,\, 6,\, 9,\, 9,\, 9,\, 9,\, 12,\, 12,\, 12,\, 12,\, 12 \right \}
a

Find the following probabilities:

i

P \left( 3 \right)

ii

P \left( 5 \right)

iii

P \left( 6 \right)

iv

P \left( 9 \right)

v

P \left( 12 \right)

b

State the number most likely to be selected.

5

Charlie enters a raffle in which 300 tickets are sold. Find the probability of him winning a prize if he purchases:

a

1 ticket

b

2 tickets

c

3 tickets

d

n tickets

6

Dave has a bag of 50 marbles, 23 of which are blue. Find the probability of Dave picking a blue marble as a percentage.

7

A bag contains 17 yellow marbles, 10 grey marbles and 14 orange marbles.

If one marble is picked at random from the bag, find the probability that it is:

a

Yellow

b

Grey

c

Orange

d

Yellow or orange

e

Grey or orange

f

Yellow, grey or orange

8

A marble is randomly drawn from a bag which contains 8 red marbles, 8 green marbles and 7 blue marbles. Find:

a

P \left( \text{red} \right)

b

P \left( \text{green} \right)

c

P \left( \text{blue} \right)

d

P \left( \text{white} \right)

9

A marble is randomly drawn from a bag which contains 6 red marbles, 7 green marbles and 3 blue marbles. Find:

a

P \left( \text{red} \right) + P \left( \text{green} \right) + P \left( \text{blue} \right)

b

P \left( \text{red or green} \right)

c

P \left( \text{red or blue} \right)

d

P \left( \text{green or blue} \right)

10

A bag contains 86 marbles, some of them are black and some are white. If the probability of selecting a black marble is \dfrac{33}{43}, find:

a

The number of black marbles.

b

The number of white marbles.

11

Balls labelled 1 to 20 are placed in a bag. If one ball is drawn at random, find the probability of drawing:

a

The number 14.

b

An even number.

c

A number higher than 6.

d

The number 8 or lower.

e

The number 5,\, 8,\, 17 \text{ or } 20.

12

Glen randomly picks one of the letters from the word \text{MINTS}.

a

How many different possible outcomes are there?

b

Find the probability that Glen picks the letter:

i

I

ii

T

13

In a standard deck of cards, find the probability of picking:

a

The ten of diamonds.

b

A spade.

c

A red card.

14

Each 26 letters of the alphabet are written on separate pieces of paper and placed in a bag. If one letter is to be picked out of the bag at random, find the probability of picking a:

a

J

b

K, Y or R

c

M, K, D, O, H or B

d

Letter in the word PROBABILITY

e

Letter in the word WORKBOOK

15

A letter is randomly selected from the alphabet. Find the following probabilities:

a

P\left(\text{J}\right)

b

P\left(\text{any letter after T}\right)

c

P\left(\text{any letter between H and N}\right)

d

P\left(\text{any letter before F}\right)

e

P \left( \text{vowel} \right)

f

P \left( \text{consonant} \right)

g

P \left( \text{consonants between H and N} \right)

h

P \left( \text{vowel between C and J} \right)

16

A three-digit number is to be formed from the digits 8, 5 and 9. Find the probability that the number formed is:

a

Odd

b

Even

c

Less than 900.

d

Divisible by 5.

17

A book has pages numbered from 1 to 100. If the book is opened to a random page, find the probability that the page number:

a

Is a multiple of 9.

b

Has the digit \rq 6 \rq in the page number.

18

A cube has six faces, each face is painted a certain colour. If the cube is rolled, find the number of faces that should be painted blue so that the probability of blue appearing on the uppermost face is:

a

\dfrac{1}{2}

b

\dfrac{1}{3}

c

\dfrac{1}{6}

d

1

19

A standard six-sided die is rolled.

a

List all the possible numbers that can be rolled.

b

Find the probability of rolling the number:

i

2

ii

6

iii

4

iv

3

v

1

c

Find the following probabilities:

i

P \left( \text{neither } 2 \text{ nor } 5 \right)

ii

P \left( \text{odd number} \right)

iii

P \left( \text{number greater than } 1 \right)

iv

P \left( \text{number divisible by } 2 \right)

v
P \left( \text{number less than } 1 \right)
vi

P \left( \text{number less than } 4 \text{ or} \text{ greater than } 6 \right)

vii
P \left( \text{number divisible by } 1 \right)
viii
P \left( \text{prime number} \right)
ix

P \left( \text{number between } 4 \text{ and } 6 \right)

x
P \left( \text{number divisible by } 2 \text{ or } 3 \right)
20

A word game uses the spinner shown:

a

List all the possible letters that can be spun.

b

How many possible outcomes are there when the spinner is spun?

c

Find the probability of spinning the letter:

i

\text{ H}

ii

\text{ S}

21

The following spinner is spun:

a

Find the probability it lands on red as a decimal.

b

Express the probability it lands on blue as:

i

A fraction in its simplest form.

ii

A percentage.

iii

A decimal.

22

Using the following spinner, find the probability of spinning:

a

3

b

7

c

6 or 8

d

A number between 1 and 3 inclusive.

e

Strictly less than 7.

23

A 12-sided die has faces with the numbers 1 through 12.

a

How many different possible outcomes are there when this die is rolled?

b

Find the probability of rolling an odd number.

c

Find the probability of rolling a multiple of 4.

24

Charlene spins the spinner shown:

a

List the sample space.

b

Find the probability of spinning a number greater than 29.

c

Find the probability of spinning a number in the twenties.

d

Find the probability of spinning a 27 or a 29.

25

A spinner is placed on the board below, and spun to land on one of the numbers. Find the following probabilities:

a

P \left(\text{multiple of } 2\right)

b

P \left(\text{multiple of } 5\right)

c

P \left(\text{multiple of } 13 \right)

d

P \left(\text{odd }\right)

e

P \left(\text{divisible by } 3 \right)

f

P \left(\text{divisible by } 7 \right)

g

P \left(\text{divisible by } 11 \right)

h

P \left(\text{prime} \right)

26

A circular spinner is divided into three unequal parts. The green sector takes up an angle of 250 \degree at the centre. The red sector takes up an angle of 60 \degree at the centre and the blue sector takes up the remainder of the spinner. Find the probability that the spinner will land on blue.

27

Consider the following figure:

a

Sarah randomly chooses a yellow shape.

i

State the number of possible outcomes.

ii

Find the probability that the yellow shape she picks is a square.

b

Sarah randomly chooses one of the squares.

i

State the number of possible outcomes.

ii

Find the probability that the square she picks is grey.

28

A Year 4 class are sitting at their desks in the order shown below. A student is chosen at random from the class.

Column 1Column 2Column 3Column 4Column 5
Row 1LauraKennethSophiaHermioneValentina
Row 2Oliver MariaHarryRoald
Row 3GwenJennyFredMario
Row 4 AaronLukeElizabethDerek
a

State the number of possible outcomes.

b

Find the probability that the chosen student is in:

i

Column 4

ii

Row 1

iii

Year 4

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solves probability problems involving multistage events

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