Probability of a single event

Example

A letter is selected at random from the word Mathematics. What is

the probability that it is:

a) a h

b) a consonant

c) a m?

Example

A bag contains 9 white balls, 8 green balls and 3 blue balls. One

ball is selected at random. What is the probability that the ball is

(a) white

(b) green

(c) red

(d) not blue?

Example

A single card is drawn from a pack of 52 playing cards. Find the

probability of the card being:

(a) a Queen

(b) a club

(c) the Jack of hearts

(d) an even number.

(e) a picture card

Example

26% of the population is overweight.

What is the probability that a person selected at random is not

overweight?

Example

Ten counters equal in size and shape are numbered 1, 2, 3, 4,

5, 6, 7, 8, 9 and 10 are placed in a bag. One counter is

selected at random. What is the probability of selecting a

counter which is

(a) numbered 3

(b) a factor of 16

(c) greater than 7?

Example

The table below shows the distribution of the ages of people

visiting a local dentist in the month of March.

A person is selected at random to answer a survey. What is

the probability that the person is aged between 15 and 30

years of age.

Age (n) 150 n 3015 n 4530 n 6045 n 7560 n

frequency 54 38 25 40 17

Example

The Bar chart below represents the favourite subjects of class

6B1.

One student is selected at random. What is the probability that

their favourite lesson is mathematics?

0

2

4

6

8

10

History Maths English Science French Art

Example

A bag contains blue, red and green cards only.

One card is taken at random from the bag.

The table shows the probabilities of taking a blue card and a red

card.

Colour Blue Red Green

Probability 0.3 0.5

(a) What is the probability of taking a yellow card from the bag?

(b) What is the probability of taking a card that is not blue from

the bag?

(c) Complete the table to show the probability of taking a green

card from the bag

Example

Emma has a box of counters.

The counters are green, red or blue.

She picks a counter at random.

The table shows the probability that she picks a green counter

and the probability that she picks a red counter.

Colour Probability

Green 0.6

Red 0.25

Blue

(a) What is the probability that Emma picks a blue counter?

(b) There are 10 red counters in the box. How many green

counters are in the box?

Relative Frequency

Example

A spinner with five edges numbered 1 to 5 is spun 20 times and the

results are shown below.

1 4 3 3 4 5 1 2 1 3

4 5 1 3 4 2 2 1 5 4

Complete the table of relative frequencies below.

Number on spinner

1 2 3 4 5

Relative Frequency

Example

The Bumbleton and Stickton village football teams have played

each other 50 times.

Bumbleton have won 10 times, Stickton have won 35 times, and

the teams have drawn 5 times.

Estimate the probability that Stickton will win the next match

Example

Matthew decides to try to estimate the probability that toast lands

butter-side-down when dropped.

He drops a piece of buttered toast 50 times and observes that it

lands butter-side-down 30 times.

Estimate the probability that the toast lands butter-side-down.

Example

A drawing pin can land 'point up' or 'point down' when

dropped.

Jim drops a drawing pin 100 times and it lands "point up"

35 times. Estimate the probability of the drawing-pin

landing "point up"

Example

A spinner has a red sector (R) and a yellow sector (Y).

R ed

Yello w

The arrow is spun 1000 times.

The table shows the relative frequency of a red

after different numbers of spins.

Number of spins Relative frequency of a red

50 0.42

100 0.36

200 0.34

500 0.3

1000 0.32

a) How many times was a red obtained after 200 spins?

b) Which relative frequency gives the best estimate of the probability of a red? Explain your answer.

Example

A dice is suspected of bias. Here are the results of 20 throws

3 4 2 3 1 5 6 2 4 3

4 3 1 1 6 2 5 6 5 3

(a) Use these results to calculate the relative frequency of each score

Score 1 2 3 4 5 6

Relative frequency

(b) Use the relative frequency to calculate how many times you would

expect to score 3 in 60 throws of this dice.

(c) Compare your answer to part (b) with the number of times you

would expect to score 3 in 60 throws of a fair dice.