Page 158 - Mathematics Coursebook

16.3 Mutually exclusive outcomes

2 Jessica throws a normal six-sided dice. Here are four different outcomes.
A: an even number B: an odd number C: more than 5 D: less than 4
a Which outcome is least likely?
b Write down three different pairs of mutually exclusive outcomes.
3 People are invited to compete to be a contestant in a television quiz show.
Here are some possible outcomes for the person who is chosen.
A: The contestant is a woman over 25 years old. B: The contestant is a man.
C: The contestant is 21 years old. D: The contestant is a 30-year-old man.
a List the possible pairs of mutually exclusive outcomes.
b List three of the outcomes that are all mutually exclusive.
c What can you say about the probabilities of B and D?

4 These are some possible outcomes for an aeroplane that is due to arrive at midday tomorrow.
A: It is late. B: It arrives at 12 35. C: It arrives before 11 45.
D: It arrives after 11 50. E: It is early.
a Are any pairs of these outcomes mutually exclusive?
If so, which pairs?
b Write down three mutually exclusive outcomes for You do not have to use the
when the aeroplane lands, one of which must happen. events listed above.
5 A fair spinner has four colours: red, green, blue and yellow.
It is spun once.
a List two possible outcomes that are mutually exclusive.
b List two outcomes that are not mutually exclusive.
c Find the probabilities of your outcomes in part b.
6 This 20-sided dice has the numbers from 1 to 20 on its faces.
All numbers are equally likely. Gavin throws the dice once.

a What is the probability that the outcome is a single-digit number?
b Find an outcome that is mutually exclusive to the outcome in part a
but has the same probability.
c Here are three different outcomes.
T: a multiple of 3 F: a multiple of 5 S: a multiple of 7
i Find the probability of each of these outcomes. Write your answer as a percentage in each case.
ii Which of these three outcomes are mutually exclusive?

16 Probability 157