Probability of Two or More Events
Probability of Two Events

When two events take place, and every outcome is equally likely to happen, the probability of a particular combined outcome can be readily found from the formula

probability =

The following examples show how this formula is used.

Worked Examples

1

Two dice are thrown together. Find the probability that the total score is 9.

Show me

The table shows all the possible outcomes and total scores.

Second dice
123456
First
dice		1234567
2345678
3456789
45678910
567891011
6789101112

There are 36 possible outcomes, and each one is equally likely to occur.

The outcomes that give a total of 9 have been circled. There are 4 such outcomes.

Now the probability can be found.

P(9) = =

2

A spinner that forms part of a children's game can point to one of four regions, A, B, C or D, when spun. What is the probability that when two children spin the spinner, it points to the same letter?

Show me

The table shows all the possible outcomes.

Second child
ABCD
First
child		AAAABACAD
BBABBBCBD
CCACBCCCD
DDADBDCDD

There are 16 possible outcomes. Each is equally likely to occur. The outcomes that are the same for both children have been circled. There are four outcomes of this type.

The probability that both have the same letter is

=

Note

It is expected that fractions are used for expressing probabilities, but using decimals is equally acceptable.

Exercises

When two coins are tossed together the possible outcomes are as shown in the table.

Second
coin
HT
First
coin		HHHHT
TTHTT
(a)

What is the probability that both coins show heads?

(b)

What is the probability that only one coin shows a tail?

(c)

What is the probability that both coins land the same way up?

A coin is tossed and a die is rolled. Copy and complete the table below to show the possible outcomes.

Dice
123456
CoinHH1
T

What is the probability of obtaining

(a)
a head and a 6,
(b)
a tail and an odd number,
(c)
a head and an even number,
(d)
a head and a number greater than 2,
(e)
an even number?

A school cook decides at random what flavour drink to serve at lunch time. She chooses from blackcurrant (B), orange (O) and lemon (L).

(a)

Complete the table to show the possible outcomes from two consecutive days.

Second day
BLO
First
day		BBB
LLO
O
(b)

What is the probability that she serves:

(i)
blackcurrant on both days,
(ii)
the same flavour on both days,
(iii)
lemon or blackcurrant on both days?
(c)

Clare will not drink lemon squash. What is the probability that she is unable to drink the squash on two consecutive days?

A young couple decide that they will have two children. There is an equal chance that each child will be a boy or a girl.

(a)

Find the probability that both children are boys.

(b)

Find the probability that both children are of the same sex.

The first diagram shows an unbiased spinner used in a game.

It is divided into five equal sections.

The arrow is spun once.

(a)

What is the probability that the arrow will land on section A?

The second diagram shows another unbiased spinner.

Section W is twice the size of each of the other sections.

(b)

What is the probability that the arrow on this spinner will land on section W?

(c)

When both arrows are spun at once, one outcome could be AW.

List the other possible outcomes.

Type Spinner ABCDE first e.g. AW not WA.

A four sided spinner is spun and a die is rolled.

The two scores are then multiplied to give a result.

(a)

Complete the table to show all the possible results.

Die
123456
Spinner1
2
3
4
(b)

The spinner is spun once and the die is rolled once.

What is the probability of getting a result of 12?