# 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 2The 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

A spinner has five possible outcomes A, E, O, P and S.
The probabilities of each outcome are shown in the table below.
OutcomeProbability
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

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Make sure you simplify all the fractions in your answers.

Question 1
A bag contains 6 red balls, 5 blue balls and 9 yellow balls. A ball is taken at random from the bag.

Work out the probability that it is:
(a) red
(b) blue
(c) yellow
(d) red or blue
(e) red or yellow
(f) blue or yellow

Question 2
In a packet of sweets there are 20 mints, 10 fudges and 20 toffees. A sweet is taken at random from the packet.

Work out the probability that it is:
(a) a fudge
(b) a toffee
(c) a mint
(d) a mint or a toffee
(e) a mint or a fudge
(f) a toffee or a fudge

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

You have now completed Unit 21 Section 6
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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