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7.03 Probability and arrays

Worksheet
Probability and arrays
1

Ben has 3 shirts, each in a different colour: crimson (C), pink (P) and white (W), and 4 ties, each in a different colour: blue (B), grey (G), red (R) and yellow (Y).

a

How many different combinations are possible?

Find the probability that he is wearing:

b

A pink shirt and yellow tie.

c

A pink shirt.

d

A pink or white shirt.

CPW
BC,BP,BW,B
GC,GP,GG,W
RC,RP,RW,R
YC,YP,YW,Y
2

A player rolls two dice and finds the sum of the numbers on the faces.

a

List the sample space for the sum of two dice.

b

Find the probability the dice will sum to five.

c

Find the probability the dice will sum to an odd number.

123456
1234567
2345678
3456789
45678910
567891011
6789101112
3

A player rolls two dice and finds the difference, that is, the largest number minus the smaller number.

a

List the sample space for the difference of two dice.

b

Find the probability the dice will have a difference of zero.

c

Find the probability the dice will have a difference of five.

123456
1012345
2101234
3210123
4321012
5432101
6543210
4

Twenty-two balls coloured either green or black and numbered 1 to 11 are placed in a bag. The table shows all the possible outcomes that can occur:

1234567891011
Green\text{G}1\text{G}2\text{G}3\text{G}4\text{G}5\text{G}6\text{G}7\text{G}8\text{G}9\text{G}10\text{G}11
Black\text{B}1\text{B}2\text{B}3\text{B}4\text{B}5\text{B}6\text{B}7\text{B}8\text{B}9\text{B}10\text{B}11

Find the probability that a ball drawn at random from the bag:

a

Is black.

b

Has the number 2.

c

Has the number 2 or 7.

d

Has a number 3 or higher.

e

Is green and has the number 5.

f

Is green or has the number 5.

5

In a boardgame a player rolls two six-sided dice but can only move the number of spaces as the largest number rolled. The table shows the possible outcomes:

a

List the sample space for the largest number rolled.

b

Find the probability a player can move 4 spaces.

c

What is the most likely number of spaces a player can move?

d

Find the probability a player moves an even number of spaces.

e

Find the probability a player can move 2 or 5 spaces.

123456
1123456
2223456
3333456
4444456
5555556
6666666
6

Two dice are rolled, and the combination of numbers rolled on the dice is recorded.

a

Complete the table of outcomes:

123456
11,11,2
22,1
3
4
5
6
b

Find the following probabilities for the two numbers rolled:

i

P(1 and 4)

ii

P(1 then 4)

iii

P(difference =4)

iv

P(product =12)

v

P(difference \leq 2)

vi

P(difference =3)

vii

P(product =20)

viii

P(difference \leq 1)

c

If the numbers appearing on the uppermost faces are added, state whether the following are true or false:

i

A sum greater than 7 and a sum less than 7 are equally likely.

ii

A sum greater than 7 is more likely than a sum less than 7.

iii

A sum of 5 or 9 is more likely than a sum of 4 or 10.

iv

An even sum is more likely than an odd sum.

7

The following two spinners are spun and the result of each spin is recorded:

a

Complete the table to represent all possible combinations:

b

State the total number of possible outcomes.

c

Find the probability that the spinner lands on a consonant and an even number.

d

Find the probability that the spinner lands on a vowel or a prime number.

ABC
11,A
22,C
3
8

The following spinner is spun and a normal six-sided die is rolled:

WXYZ
11,W
22,Z
3
4
55,X
6
a

Complete the table above to represent all possible outcomes.

b

State the total number of possible outcomes.

c

Find the probability that the spinner lands on X and the die rolls a 1.

d

Find the probability that the spinner lands on W and the die rolls an odd number.

e

Find the probability that the spinner doesn’t land on Z and the die rolls an even number.

9

A coin is tossed and a die is rolled simultaneously.

a

Complete the following table to display the possible outcomes:

123456
Heads\text{H,1}\text{H,3}\text{H,4}\text{H,6}
Tails\text{T,2}\text{T,3}\text{T,5}
b

How many possible outcomes are there?

c

Determine the probability of rolling a 1.

d

Determine the probability of rolling an even number.

e

Determine the probability of tossing a head and rolling an even number.

10

Box A contains 2 red and 2 blue marbles while Box B contains 1 green, 2 yellow and 1 red marbles. A marble is randomly selected from each box.

a

Complete the given table to represent all possible outcomes:

b

Determine the probability of:

i

Drawing marbles the same colour.

ii

Drawing marbles of different colour.

iii

Drawing a red and a yellow marble.

iv

The draw containing at least one red marble.

GYYR
RR,GR,YR,R
RR,YR,R
BB,GB,YB,R
BB,YB,Y
11

The following spinner is spun and a normal six-sided die is rolled at the same time. The product of their respective results is recorded.

a

Construct a table to represent all possible outcomes.

b

State the total number of possible outcomes.

c

Find the probability of an odd product.

d

Find the probability of rolling a 5 on the dice and scoring an even product.

e

Find the probability of spinning a 3 on the spinner or scoring a product which is a multiple of 4.

12

The following two spinners are spun and the sum of their results is recorded:

Spinner 1

Spinner 2

a

Construct a table to represent all possible outcomes.

b

State the total number of possible outcomes.

c

Find the probability that the first spinner lands on an even number and the sum is even.

d

Find the probability that the first spinner lands on a prime number and the sum is odd.

e

Find the probability that the sum is a multiple of 4.

13

Two spinners labelled 1 to 4 are spun simultaneously and the results added:

Spinner 1

Spinner 2

a

Construct a table to represent all possible outcomes.

b

List the sample space for the sum of the two spinners.

c

Determine the probability of:

i

An even result.

ii

A result greater than 6.

iii

A result less than 5 and even.

iv

A result less than 5 or even.

14

A two-digit number is formed by spinning the following two spinners with Spinner 1 being the first digit and Spinner 2 being the second digit in the number:

Spinner 1

Spinner 2

a

Construct a table to represent all possible outcomes.

b

Determine the probability the number formed:

i

Is 25.

ii

Is even.

iii

Is prime.

iv

Is divisible by 5.

v

Is divisible by 5 and odd.

vi

Contains at least one 2.

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Outcomes

4.1.8

use a sample space to determine the probability of outcomes for an experiment

4.1.9

use arrays or tree diagrams to determine the outcomes and the probabilities for experiments

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