Download Homework 22: Support: Probability

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a
Explain how fractions can be added and subtracted. Give some
examples.
b
A spinner has sections labelled A, B, C and D. The
probability of getting A is
getting B is
2
1
5
1
4
, and the probability of
. What is the total of the probabilities of A and B?
2
7
c
The probability of winning a game is
a
Explain how multiplying a fraction by a whole number can help you to work out the
expected number of successes when an experiment is repeated. Give an example.
b
The probability of winning a game is
3
5
. What is the probability of not winning?
. How many wins would you expect if you played
the game 100 times?
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A discount electrical store sells a brand of kettle with a probability of 0.32 that it contains a fault.
Jenny buys two of these kettles for her work staff-room.
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a
Draw a tree diagram to show all the possible outcomes.
b
What is the probability that both kettles are faulty?
c
What is the probability that only one of the kettles contains a fault?
a
Draw a tree diagram to show the possible outcomes when a fair coin is tossed twice. Use your
tree diagram to work out the probability of getting Heads both times.
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b
Carry out an experiment to estimate the experimental probability of getting two Heads
when a coin is tossed twice. Decide how many trials you need in the experiment. Calculate
the experimental probability of getting two Heads.
c
Write a short report explaining how you designed and carried out your experiment. Give
your results and explain whether or not the experimental and theoretical probabilities are in
agreement with each other.
a
Draw a tree diagram to show the possible outcomes when a fair coin is tossed three times.
b
What is the probability of getting
i
3 Heads
ii
2 Heads and 1 Tail (in any order)?
EXTENSION LEVEL 6/7
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At the ‘Hook-A-Duck’ stall at a school fete, children use a rod with a hook at the
end to catch a duck floating in a large bowl of water.
The underside of each duck is marked either S for star prize, W for win
or L for lose. After a duck has been hooked it is always returned to the
water before another duck is hooked.
a
For the trial ‘hooking-a-duck’, list the outcomes in the sample space.
b
For the trial described in a discuss whether or not you think the
outcomes will be equally likely.
In the bowl there is 1 duck marked S, 9 marked W and 2 marked L.
c
Write down the theoretical probability of the following
events.
i
Winning the star prize
iii Winning something
v
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ii
Not winning the star prize
iv
Not winning any prize
Just a win
Another stall at the school fete has this board:
PRIZE!
1
2
3
4
5
You throw a dice.
You win a prize if your score is 5.
You win a penny sweet if your score is an even number.
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a
List the outcomes in the sample space.
b
Write down the theoretical probability of the following
events.
i
winning something
iii not winning the prize
ii
not winning anything
iv not winning a penny sweet
Three fair tetrahedral dice X, Y and Z are thrown at the same time.
The numbers on dice X are 1, 5, 5, 1
The numbers on dice Y are 4, 4, 4, 0
The numbers on dice Z are 2, 2, 6, 2
Copy and complete the tree diagram to
show the different probabilities
of the possible outcomes when these three
dice are thrown.
The scores shown on each dice are added
together.
a
What is the highest possible score?
b
Work out the probability of getting
the highest possible total score.
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