Probability of a single event

1
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?
2
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?
3
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
4
Example 26 of the population is overweight. What
is the probability that a person selected at
random is not overweight?
5

• 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
• numbered 3
• a factor of 16
• greater than 7?

6
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.
7
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?

8
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?
• 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

9
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?
10
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
11
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
12
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.
13
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"
14
Example A spinner has a red sector (R) and a
yellow sector (Y).
The arrow is spun 1000 times.The table shows the
relative frequency of a red after different
numbers of spins.

1. How many times was a red obtained after 200
   spins?
2. Which relative frequency gives the best estimate
   of the probability of a red? Explain your answer.

15
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.