O LevelMathsCambridgeTopic QuestionsProbabilityProbability Toolkit

Probability Toolkit (Cambridge O Level Maths)

Topic Questions

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1
Sme Calculator2 marks

Sofia has a bag containing 8 blue beads and 7 red beads only.
She takes one bead out of the bag at random and replaces it.
She does this 90 times.
 
Find the number of times she expects to take a red bead.

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2
Sme Calculator3 marks

One of the teachers at a school is chosen at random.

The probability that this teacher is female is  3 over 5

There are 36 male teachers at the school.

Work out the total number of teachers at the school.

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3
Sme Calculator3 marks

Rhiana plays a game.

The probability that she will lose the game is 0.32
The probability that she will draw the game is 0.05

Rhiana is going to play the game 200 times.

Work out an estimate for the number of times Rhiana will win the game.

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4
Sme Calculator3 marks

The table shows the probabilities that a biased dice will land on 2, on 3, on 4, on 5 and on 6

Number on dice 1 2 3 4 5 6
Probability   0.17 0.18 0.09 0.15 0.1

Neymar rolls the biased dice 200 times.

Work out an estimate for the total number of times the dice will land on 1 or on 3.

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1
Sme Calculator2 marks

The probability that a sweet made in a factory is the wrong shape is 0.0028.
One day, the factory makes 25 000 sweets.
 
Calculate the number of sweets that are expected to be the wrong shape.

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2
Sme Calculator2 marks

The probability that Kim wins a game is 0.72 .
In one year Kim will play 225 games.

Work out an estimate of the number of games Kim will win.

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3
Sme Calculator1 mark

Sushila, has a bag which contains 10 red balls and 8 blue balls.
Sushila takes one ball at random from her bag.
 
Find the probability that she takes a red ball.

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4
Sme Calculator1 mark

The time taken for each of 120 students to complete a cooking challenge is shown in the table.

 Time (t minutes) 20 less than t less or equal than 25 25 less than t less or equal than 30 30 less than t less or equal than 35 35 less than t less or equal than 40 40 less than t less or equal than 45
 Frequency 44 32 28 12 4

A student is chosen at random.

Find the probability that this student takes more than 40 minutes.

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5
Sme Calculator1 mark

The frequency table shows information about the time, m minutes, that each of 160 people spend in a library.

Time (m minutes) 0 less than m less or equal than 10 10 less than m less or equal than 40 40 less than m less or equal than 60 60 less than m less or equal than 90 90 less than m less or equal than 100 100 less than m less or equal than 120
Frequency 3 39 43 55 11 9

Find the probability that one of these people, chosen at random, spends more than 100 minutes in the library.

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1a
Sme Calculator2 marks

A bag contains 7 red discs, 5 green discs and 2 pink discs.

Helen takes one disc at random, records the colour and replaces it in the bag.
She does this 140 times.
 
Find how many times she expects to take a green disc.

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1b
Sme Calculator2 marks

Helen adds 9 green discs and some pink discs to the discs already in the bag.
The probability of taking a green disc is now 2 over 7.
 
Find the number of pink discs that Helen added to the bag.

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2
Sme Calculator3 marks

There are only blue counters, green counters, red counters and yellow counters in a bag.

Olga is going to take at random a counter from the bag.

The table shows the probability that Olga will take a blue counter and the probability that she will take a yellow counter.

Colour blue green red yellow
Probability 0.4     0.15


The number of red counters in the bag is 4 times the number of green counters in the bag.

Complete the table.

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3a
Sme Calculator4 marks

There are some counters in a bag.
The counters are red or white or blue or yellow.

Bob is going to take at random a counter from the bag.

The table shows each of the probabilities that the counter will be blue or will be yellow.

Colour red white blue yellow
Probability     0.45 0.25


There are 18 blue counters in the bag.

The probability that the counter Bob takes will be red is twice the probability that the counter will be white.

Work out the number of red counters in the bag.

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3b
Sme Calculator1 mark

A marble is going to be taken at random from a box of marbles.
The probability that the marble will be silver is 0.5

There must be an even number of marbles in the box.

Explain why.

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4a
Sme Calculator1 mark

Four friends each throw a biased coin a number of times.
The table shows the number of heads and the number of tails each friend got.

  Ben Helen Paul Sharif
heads 34 66 80 120
tails 8 12 40 40


The coin is to be thrown one more time.

Which of the four friends' results will give the best estimate for the probability that the coin will land heads?
Justify your answer.

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4b
Sme Calculator2 marks

Paul says,

"With this coin you are twice as likely to get heads as to get tails."

Is Paul correct?
Justify your answer.

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4c
Sme Calculator2 marks

The coin is to be thrown twice.

Use all the results in the table to work out an estimate for the probability that the coin will land heads both times.

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5
Sme Calculator4 marks

Becky has a biased 6-sided dice.

The table gives information about the probability that, when the dice is thrown, it will land on each number.

  Number 1 2 3 4 5 6
  Probability 2 x 0.18 2 x 3 x 0.26 x

Becky is going to throw the dice 200 times.

Work out an estimate for the number of times that the dice will land on an even number.

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