PROBABILITY
Key Words Meaning
Event Example : Rolling an odd number on a dice or
winning a football match
Events can have a number of different outcomes.
outcome An outcome is a single, distinct result of a random
experiment or trial.
mutually exclusive from others.
Mutually Exclusive meaning that only one outcome can occur on each trial of
the experiment.
Example: When flipping a coin,
unlikely Impossible to describe the likelihood that an event
will happen
probability An event that is certain to happen has a
probability of 1.
An outcome that is impossible has a probability of
0.
The probability of an outcome is the likelihood of that
outcome occurring.
Sample space The set of all possible outcomes of an experiment is
called the sample space.
Example : sample space of flipping a coin is head and tail
You can write a probability as a fraction, a decimal or a percentage.
For example, an even chance means a probability of 0.5 or ½ or 50%.
Examples :
1. Tigers and Lions are two football teams.
The probability that Tigers will win their next match is 45%.
The probability that Lions will win their next match is 4/5
a Which team is more likely to win their next match? Give a reason
for your answer.
2. The probability of rain tomorrow is 25%.
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The probability of sunny weather tomorrow is 60%.
a Write both probabilities as fractions.
b Show each weather event’s probability on a probability scale .
3. Here are the probabilities that three teams will win their next
match.
City 2/3, Rovers 60%, United 0.7
a Which team is most likely to win? Give a reason for your answer.
b Which team is least likely to win?
Mutually exclusive outcomes:
4. A weather forecast says that the probability of rain tomorrow is
20% and the probability of strong winds tomorrow is 30%.
a Explain why rain and strong winds are not mutually exclusive
outcomes.
b Explain why rain and strong winds are not equally likely outcomes .
5. The names of six boys and four girls are put in a bag. One of the
boys’ names is Blake. One of the girls’ names is Crystal. One name is
chosen without looking.
a Work out the probability that the name chosen is:
i Blake ii a boy’s name iii a girl’s name iv not Crystal v a boy’s name
or a girl’s name
b Explain why the chosen name is 50% more likely to be a boy’s than
a girl’s name.
6.
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8. Caleb has a set of cards. Each card has a number on it. The cards
are placed face down and he takes a card without looking. The
probability that the chosen card is 3 is 1/3. The probability that the
chosen card is 4 is 1/4
a Find a possible list of Caleb’s cards.
b What can you say about the number of cards in the set?
c An-Mei has a different set of cards, where each card has a number
on it. She places them face down and takes a card without looking.
In her set, the probability that the chosen card is 4 is ¼ and the
probability that
the chosen card is 5 is 1/5
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What can you say about An-Mei’s set?
d Could An-Mei have the same set as Caleb?
9.
b This is not a good way to estimate the probability. Why?
c Compare your answer to part b with a partner’s answer. Have you
both given the same explanation? Can you improve your explanation?
10. Varun flips a coin. The two possible outcomes are heads and tails.
a If the outcomes are equally likely, what are the theoretical
probabilities of each outcome?
b Varun’s results are shown in the table.
Use the results to find the relative frequency of each outcome.
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c Varun’s friend Toby says that Varun is not flipping the coin fairly
because the probabilities from the experiment are incorrect.
What does Toby mean? Do you think Toby is correct?
11. A bag contains one white ball, one black ball and some red balls.A
ball is chosen
a If there are three red balls, work out the theoretical probability of
choosing each colour. Daniella takes out one ball, records the colour
and replaces it in the bag. She does this 50 times. She records her
results in a table
b Use the results to find the experimental probability of choosing each
of the three colours.
c Daniella knows that there are an odd number of red balls.
What is the most likely number? Give a reason for your answer .
Homework:
1. A computer simulates spinning three coins 160 times and records
the number of heads. Here are the results.
a Work out the experimental probability of getting:
i three heads ii three tails iii at least two heads
A teacher says: ‘The theoretical probability of getting three heads
is 1/8”.
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b How does the theoretical probability compare to the experimental
probability of getting three heads?
c What can you say about the theoretical and experimental
probabilities for getting zero heads
2. A computer simulates throwing two dice and adding the scores
together. It does this 100 times. Here are the results
a Work out the experimental probability of getting:
i7 ii more than 7 iii less than 7 iv 12
b Do you think that 100 trials is enough to get reliable results? Give a
reason for your answer.
i getting a head on the first spin
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ii needing exactly three spins until a head appears
iii needing more than three spins until a head appears
b Does 100 trials give a good estimate of the experimental
probabilities of
needing different number of spins? Explain your answer.
4.
a a female student wants to be an engineer
b a male student wants to be a lawyer
c a female student does not want to be an accountant
