Basic Probability (Cambridge International IGCSE Mathematics): Exam Questions

Jian has a fair spinner in the shape of a regular hexagon. The spinner is numbered 2, 2, 3, 4, 4, 5.

Jian spins the spinner. Find the probability that the spinner lands on

i) an even number,

ii) a number less than 6,

iii) the number 1.

Paul has a set of 8 cards, each with a number written on it.

The numbers on the cards are 1, 1, 2, 3, 3, 3, 4, 5. One card is taken at random.

Write down the probability that the number on the card is

i) 1,

ii) an odd number,

iii) a prime number,

iv) a number less than 6.

Joel spins a fair five-sided spinner numbered 2, 3, 4, 5 and 6.

Write down the probability that the spinner lands on

i) an odd number,

ii) a prime number,

iii) the number 7.

Soraya makes 30 flags. 11 flags are pink, 7 are yellow, 5 are blue, 4 are silver and 3 are green. Soraya takes a flag at random.

Find the probability that the flag she takes is

i) pink,

ii) not blue,

iii)red.

A bag contains 3 green balls, 4 red balls and 1 blue ball only. Matt takes a ball from the bag at random.

Some probabilities are marked on the probability scale.

Write down the letter that shows the probability that

Matt takes a red ball,

Extract:

A bag contains 3 green balls, 4 red balls and 1 blue ball only. Matt takes a ball from the bag at random.

Matt does not take a blue ball.

A bag contains 6 red balls and 10 blue balls only.

On the probability scale, draw an arrow ( $\downarrow$) to show the probability that a ball taken at random is

blue,

Extract:

A bag contains 6 red balls and 10 blue balls only.

red or blue.

A bag contains green balls and red balls only. A ball is taken at random from the bag. The probability of taking a green ball is 0.38.

Write down the probability of taking a red ball.

Extract:

A bag contains green balls and red balls only.

Write down the probability of taking a blue ball.

A box contains 22 coloured pencils. 6 pencils are pink, 9 pencils are blue and 7 pencils are yellow.

A pencil is taken at random from the box.

Write down the probability that this pencil is green.

The probability that Alex wins a prize is 0.27 .

Find the probability that Alex does not win a prize.

The probability that it will be sunny tomorrow is 0.97.

Work out the probability that it will not be sunny tomorrow.

The probability that it rains tomorrow is 0.35 .

Work out the probability that it does not rain tomorrow.

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 ($\downarrow$ ) to show the probability that this ball is red.

COMMONWEALTH

Lindon picks a letter at random from this word. Explain why the probability that he picks a letter M is not $\frac{1}{10}$.

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.

In a group of 40 students,

• 24 students like football
• 19 students like cricket
• 10 students like football but not cricket.

Complete the Venn diagram.

$E$ = {$x$ : $x$ is a positive integer less than 20} A = {$x$ : $x$ is an even number} B = {$x$ : $x$ is a multiple of 3}

i) Write down n $( A )$.

ii) List the elements of set $B$.

$B$= { ............................................... } [2]

One of these 19 numbers is picked at random.

Work out the probability that this number is

iiia) not in set $A$ and not in set $B$,

iiib) in $A\cup B$

iv) Complete the statement.

$A \cap B = \{ x : x \text{is} ............................... \}$

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.

Extract:

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

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,

ii) a number greater than 2.

Extract:

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

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 $\frac{1}{5}$.

Write down the probability that Dan walks to school.

Extract:

The probability that he cycles to school is 1 fifth.

There are 200 days in a school year.

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

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 $\frac{3}{14}$ 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 ($\downarrow$) on the probability scale to show the probability that Rui takes

a red pen,

Extract:

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.

a red pen or a blue pen.

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.

A bag contains counters that are red, blue, green or yellow.

The table below shows the probabilities that a counter taken at random is red, blue or yellow.

Work out the probability that the counter is red or yellow

Extract:

A bag contains counters that are red, blue, green or yellow.

The table below shows the probabilities that a counter taken at random is red, blue or yellow.

Colour

Red

Blue

Green

Yellow

Probability

0.32

0.2

0.16

Work out the probability the counter is green.

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.

iib) more than 5.

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,

ii) green or red,

iii) yellow.

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.

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

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

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.

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.

Jack has a chest full of toys.

He picks a toy at random from the chest.

The probability he picks a red toy is 0.8.

Work out the probability he picks a toy that is not red.

The chest contains three colours of toys: red, blue, and green.

Complete the table below.