Transcript Probability of a single event

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.
Age (n)
frequency
0  n  15
15  n  30
30  n  45
45  n  60
60  n  75
54
38
25
40
17
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.
Example
The Bar chart below represents the favourite subjects of class
6B1.
10
8
6
4
2
0
History
Maths
English
Science
French
Art
One student is selected at random. What is the probability that
their favourite lesson is mathematics?
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
Probability
0.3
0.5
Green
(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
Relative
Frequency
1
2
3
4
5
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).
The arrow is spun 1000 times.
The table shows the relative frequency of a red
after different numbers of spins.
Red
Yellow
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.