Unit 21 Section 6 : Addition Law for Mutually Exclusive Events

Two events are mutually exclusive if only one can happen in any given experiment.

Example 1
A bag contains red balls and yellow balls.
When a ball is taken out it is either red or yellow, but it cannot be both.
The events 'red ball' and 'yellow ball' are therefore mutually exclusive.

Addition Law for Mutually Exclusive Events If there are two events, A and B, such that the probability of A happening is P(A) and the probability of B happening is P(B), and if A and B are mutually exclusive, then: P(A or B) = P(A) + P(B)

Example 2 The probability of my team winning is	2	and the probability of them getting a draw is	5	for a particular match.
	9		9

The two events win and draw are mutually exclusive, so to work out the probability of winning or drawing, we add the probabilities together:

P(win OR draw) = P(win) + P(draw) =	2	+	5	=	7
	9		9		9

Practice Question

Outcome Probability A 2 19 E 3 19 O 7 19 P 5 19 S 2 19

Work out the answer to each of the questions below then click on the button marked to see whether you are correct. The spinner is spun once to select a letter. (a) Find P(A or E is selected) (b) Find P(O or S is selected) (c) Find P(a vowel is selected)

Exercises

Make sure you simplify all the fractions in your answers.

Question 3
A group of children were asked their ages. These are recorded in the table below:

Work out the probability that a child selected at random from the group is:

(a) age 10
(b) age 10 or 11
(c) age 12 or 13
(d) age 11 or 12

Question 4
In the school canteen, children can choose one of baked potato, chips or rice with their lunch.

The probability of a baked potato is	1	, the probability of chips is	2	, and the probability of rice is	1	.
	6		3		6

Work out the probability that a child chooses:

(a) rice or baked potato
(b) rice or chips
(c) chips or baked potato

Question 5
Zahra buys a mobile phone with 5 different coloured covers.
The probability of her using each cover is given in the table below:

	Work out the probability that cover she chooses is:
	(a) red or pink
	(b) green or red
	(c) yellow or blue
	(d) pink or yellow

Question 6
Alex can walk to school, cycle to school or go by bus.

The probability that he walks or cycles to school is	3	.
	4

The probability that he cycles to school is	1	.
	4

Work out the probability that he:

(a) walks
(b) goes by bus
(c) cycles or goes by bus

Question 7
A bus can arrive early, on time or late.

The probability that it is late is	1	.
	4

The probability that it is on time or late is	2	.
	3

Work out the probability that bus is:

(a) on time
(b) early or on time