• Subjective probabilities are probabilities based on opinions or judgements. All of the facts may not be known and we make the best prediction we can.
eg ‘There is a high probability of rain tomorrow.’
I would have more confidence in this judgement if it were given by a meteorologist than if it were given by my son.
• Assessments of the probability of success of Penrith or St George as they play each other will vary greatly according to the bias of the person asked. A more accurate assessment of the chance of success for each team would come from an unbiased observer who has studied the form of each team.
• Remember that the most likely outcome will not always occur.
The numbers 1 to 6 were written on six counters and placed in a jar.
Two of these counters are to be chosen at random.
a List all possible outcomes of this experiment.
Worked example
Rhonda and Alan had three girls. Rhonda was expecting their fourth child.
‘I hope this child is a boy,’ said Alan.
‘After three girls, it’s almost sure to be a boy,’ said a friend.
Is the friend’s reasoning correct?
Solution
• For each birth, the chance of a boy will always be irrespective of the number of girls previously born.
So the friend’s reasoning is not correct.
• There is a chance, however, that the opposite is true.
Some males may have a larger percentage of sperm of one sex. The probability of having a girl may be much higher than . Only medical tests could reveal this.
1 2
---1 2
---Numbers 1 to 6
2 6 31
5 4
Exercise 4:01
1
Choose a label from those on the right to answer each question below.
For the experiment of the six counters in the jar on page 97, what is the chance that:
b the numbers 0 and 1 are picked?
c the numbers 5 and 6 are picked?
d two numbers less than 10 are picked?
e the first number selected will be even?
f the sum of the numbers will be odd?
Using the diagrams above, list all possible outcomes if:
a the spinner is spun once
b the two dice are thrown and the numbers on the upper faces added c two balls are drawn from the container at random
d two cards are chosen at random
The spinner above is spun once. Choose the label to the right that best describes the probability that the number will be:
a 1 b not 8 c more than 5
d odd e 0 f less than 10
The dice above are thrown. Choose the label that best describes the probability that the sum of the top numbers will be:
a 12 b less than 12 c less than 6
d even e 1 f less than 15
A coloured ball is drawn at random from the container above.
Which label best describes the probability that the ball is:
a blue? b green?
c red? d coloured?
Write the events in parts a to d in order, from least likely to most likely.
Two cards are drawn at random from the five above. Which label best describes the probability that the cards:
a are both fives?
b have a sum equal to 15?
c have a sum greater than 9?
d are both larger than 9?
Write the events in parts a to d in order, from least likely to most likely.
Australia is playing cricket against England at the Sydney Cricket Ground.
a From the list below, select the five factors that you think would most influence the outcome of the match. Give a reason for each choice.
• The colour of the uniforms
• Who wins the toss
• The recent form of the players
• The number of tickets sold
• The country where it is played
• The condition of the wicket
• The weather
• The choice of umpires
• The length of the grass
• The ability of the captains b Who do you think would win?
Give a reason for your answer.
c If Australia has never lost in Sydney, is it possible that Australia will lose?
d Are the only possible outcomes: Australia wins or Australia loses? Explain your answer.
Is each statement reasonable or not? Discuss the reasoning in each case.
a On my last four attempts, I have failed to lift this weight. I’m sure to succeed this time.
b My diamond ring is in one of these three jewellery boxes. I have searched two and it is not in them.
It must be in the third one.
c We almost pushed the car out of the bog that time.
Now that Chub is here to help, I’m sure we will get it out this time.
d The first three puppies were female. The next is sure to be male.
e I’ve turned 48 cards of this pack and have turned only one ace. The next card I turn is sure to be an ace.
f I’ve just heard that a fire storm has passed through our street. I fear our home has been destroyed.
g I’m glad it’s raining today because that means it won’t rain for tennis tomorrow.
Discuss the contradictory nature of these statements.
a The horse was a certainty beaten.
b I was so close to winning the lottery. My number was 908 146. The winning number was 808 146.
c The winner came from an impossible position.
Comment critically on the statement: ‘Since there are 26 letters in the English alphabet, the probability that a person’s name starts with X is 1 in 26’.
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