Browse Basic probability

45 questions at your level

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

Probability of a single event

16 questions

LessonNot started

A bag contains only blue beads, green beads and white beads.

A bead is taken at random from the bag.

The probability that the bead is blue is

\frac{1}{4}

.

The probability that the bead is green is three times the probability that the bead is white.

(a) Work out the probability that the bead is white.

There are 96 beads in the bag.

(b) Work out the number of green beads in the bag.

Alex takes a bead at random, records its colour and puts it back. He does this 96 times.

Alex says, "The number of times I record a green bead will be exactly the same as the number of green beads in the bag."

(c) Explain why Alex is wrong.

●●●●●Level 57 marksStart

Sample space & systematic listing

16 questions

LessonNot started

A four-digit code is made using these rules:

the first digit must be odd,
the last digit must be $0$ or $5$ ,
the second and third digits can be any digit from $0$ to $9$ .

Digits may be repeated.

(a) Work out how many different codes are possible.

(b) A code is chosen at random from all the possible codes. Find the probability that all four of its digits are the same.

●●●●●Level 55 marksStart

In a football league every team plays every other team exactly once. Altogether

45

matches are played.

(a) Work out how many teams are in the league.

(b) One of the

45

matches is chosen at random. Rovers is one of the teams in the league.

Find the probability that the chosen match is one that Rovers plays in.

●●●●●Level 55 marksStart

5

white counters,

3

purple counters and

2

black counters in a bag.

Omar takes at random three counters from the bag.

Work out the probability that the bag is then left with more black counters than purple counters.

You must show all your working.

(5 marks)

●●●●●Level 55 marksStart

12

1

12

in a tin.

Hana will take at random two discs from the tin.

Hana says,

"The probability that the sum of the two numbers is odd is twice the probability that their product is odd."

Is Hana correct?

You must show how you get your answer.

(5 marks)

●●●●●Level 55 marksStart

Relative frequency & expected outcomes

14 questions

LessonNot started

A company tests a sample of

500

of its light bulbs.

12

of them fail within a year.

(a) Use this sample to estimate the probability that a bulb fails within a year.

(b) The company sells

25\,000

bulbs. Every bulb that fails within a year is replaced, at a cost of £

3.50

to the company. Estimate the total replacement cost.

(c) The company then tests a second sample of

1500

bulbs, of which

27

fail within a year. Use both samples to give a better estimate of the probability that a bulb fails within a year.

(d) Explain why your answer to part (c) is a better estimate than your answer to part (a).

●●●●●Level 58 marksStart