Introduction to Probability (OCR GCSE Maths: Foundation): Exam Questions

Sarah throws a biased dice 10 times.
She gets 8 sixes.

Diljit throws the same dice 50 times.
He gets 41 sixes.

Jonah is going to thrown the dice once.

i) Whose results will give the better estimate for the probability that Jonah will throw a six, Sarah's or Diljit's?
You must give a reason for your answer.

ii) Use Sarah's and Diljit's results to work out an estimate for the probability that Jonah will throw a six.

Spinner A is a fair four-sided spinner labelled 1, 2, 3 and 4.

Spinner B is a fair five-sided spinner labelled 1, 2, 3, 4 and 5.

A student spins both spinners and multiplies the two numbers together to get the product.

Complete the sample space diagram to show all the possible products.

(Spinner A values are listed down the rows; Spinner B values are listed across the columns.)

Find the probability that the product is a square number.

A bag contains 20 balls.
5 of these balls are red.
A ball is picked at random from the bag.

On the probability scale, draw an arrow ( ) to show the probability that this ball is red.

A student spins a fair five-sided spinner and flips a fair coin.

The spinner has sides numbered .

The coin can land on heads (H) or on tails (T).

Complete this table to show all the possible outcomes.

Find the probability of getting heads with a number greater than 5.

Give your answer as a fraction in its simplest form.

COMMONWEALTH

Lindon picks a letter at random from this word.
Explain why the probability that he picks a letter M is not .

Tickets for athletics or swimming or hockey or diving are placed in a box.
A ticket is picked at random from the box.

Complete the table.

On any day, the probability that Marcus will get a seat on the school bus is 0.93 .

Write down the probability that he will not get a seat on the school bus today.

There are 200 school days in a year.

Work out the expected number of days in a year that Marcus will not get a seat.

The diagram shows a fair 8-sided spinner.

The numbers on the spinner are 3, 4, 4, 7, 7, 7, 8 and 9.

The spinner is spun once.

Write down the probability that the spinner lands on

i) the number 7,

[1]

ii) a number greater than 2.

[1]

The spinner is spun 160 times.

Work out the expected number of times the spinner lands on the number 7.

................................................. 

Dan either walks or cycles to school.
The probability that he cycles to school is .

Write down the probability that Dan walks to school.

There are 200 days in a school year.

Work out the expected number of days that Dan cycles to school in a school year.

[1]

Marco has ropes of four different colours.
He takes a rope at random.

Complete the table.

The probability that a sweet made in a factory is the wrong shape is 0.0028 .
One day, the factory makes 25000 sweets.

Calculate the number of sweets that are expected to be the wrong shape.

Records show that  of all mullet caught are underweight.

In one day, 168 mullet are caught.

Work out the expected number of mullet that are underweight.

Rui has a bag containing 5 black pens, 8 red pens and 3 blue pens only.
He takes a pen out of the bag at random.

Draw an arrow () on the probability scale to show the probability that Rui takes

a red pen,

a red pen or a blue pen.

A fair spinner has red and blue edges only.

The probability that the spinner lands on red is .

Find the probability that the spinner lands on blue.

The spinner is spun 80 times.

Find how many times you would expect the spinner to land on red.

The probability that Tommy has his calculator for his mathematics lesson is 0.4 .
There are 120 mathematics lessons in one year.

Work out an estimate of the number of mathematics lessons in one year that Tommy has his calculator.

Jen, Geoff and Alesha play a game with a toy that has an arrow painted on it.
When the toy is thrown it can land with the arrow pointing up or the arrow pointing down.
The toy is thrown a number of times.

The table below shows the number of times that the toy landed with the arrow pointing up and the arrow pointing down for each person.

  Priti is going to throw the toy once.

Whose results will give the best estimate for the probability that the toy will land with the arrow pointing down?
Give a reason for your answer.

Bryce is going to throw the toy two times.

Use all the results in the table to work out an estimate for the probability that the toy lands with the arrow pointing up on both throws.

Mei has two fair square spinners, A and B.
Spinner A is numbered 1, 2, 2, 4 and spinner B is numbered 3, 3, 4, 5.

She spins both spinners and adds the two numbers.

i) Complete the table to show all the possible outcomes.

Use the table to write down the probability that the total is

iia) 5.

[1]

iib) more than 5.

[1]

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.

A bag contains 6 green balls, 5 red balls and 3 blue balls only.
A ball is taken from the bag at random.

Find the probability that the ball is

i) green,

[1]

ii) green or red,

[1]

iii) yellow.

[1]

Another bag contains brown balls, white balls, black balls and purple balls only.
A ball is taken from this bag at random.

i) Complete the table.

[2]

ii) Which colour is the most likely to be taken?

[1]

iii) There are 50 balls in this bag.
Work out the number of black balls.

[1]

A box contains 3 blue pens, 4 red pens and 8 green pens only.
A pen is chosen at random from the box.

Find the probability that this pen is green.

A cube has only one of its six faces painted yellow.
This cube is rolled 240 times.

Work out the expected number of times that it lands on the yellow face.

[1]

Reece is playing a computer game.

He can score 0, 5, 10 or 15 points on each turn.

Reece records his scores for 100 turns.

The table shows the relative frequencies of his scores.

Complete the table.

Reece says

I scored more than 700 points in total in my 100 turns.

Is Reece correct?

Show how you decide.

The probability that Zoe feeds the ducks when she visits the lake is 0.82.
Zoe visits the lake 200 times in one year.

Work out an estimate of the number of times that Zoe does not feed the ducks when she visits the lake.

A bowl only contains apples, oranges and pears.

A piece of fruit is picked at random from the bowl.

• The probability of picking an apple is .

• There are 12 pears.

• The probability of picking an orange is 4 times as likely as picking a pear.

Work out the total number of pieces of fruit in the bowl.