Download `USING PROBABILITY TO DESCRIBE SITUATIONS`

Numeracy
Application of Number
______________
L1
Workbook 16
Probability
HD2/L1.1
HD2/L1.2
basic & keySKILLBUILDER
Handling Data
Probability
HD2/L1.1,2
Using probability to describe situations
Probability is measured on a scale of 0 to1
If an event is certain to happen then it is said to have a probability of 1 or 100%.
If an event is certain not to happen then it is said to have a probability of 0 or 0%.
If an event may or may not happen then it will have a probability somewhere between 0 - 1 or
0 - 100%.
We use probability to describe the likelihood of a situation occurring.
It can be written as a fraction, decimal or percentage.
Some examples:
a) There is a 70% chance it will rain tomorrow.
b) The probability of getting a head when you toss a coin is
c)
1
or 0·5.
2
It is 99% certain that Mansfield town will win the league!
d) There is a 0·1% chance it will rain in June.
Workbook 16
Level 1 Numeracy/Application of Number
2
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Probability
HD2/L1.1, 2
Calculating the probability of equally likely outcomes
Example 1
What is the chance of picking up a red card from a pack of cards.
 there are 52 cards.
26 are red.
So the probability is 26 out of 52.
Which we write as
26 1

52 2
or a one in two chance
It can also be expressed as a percentage (50% chance).
or decimal fraction 0.5
or fifty – fifty chance
Probability of an
event occurring
=
number of successful ways
total number of all possible ways
Example 2
You have six cups, one of which has a chip in it. What is the chance of taking that cup out
of the cupboard for your guest?
There are 6 cups
1 is chipped
So the probability is 1 out of 6
(you have 6 to choose from and you happen to choose the 1 that is chipped)
this may also be written:
1
6
16.66%
0.17 (rounded to 2 d.p.)
N.B. Sometimes an event is impossible. (Throwing a 7 with a die).
Workbook 16
Level 1 Numeracy/Application of Number
3
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Probability
HD2/L1.1, 2
Exercise 1 (Express your answers as fractions)
1.
A die is rolled. Calculate the probability that the result will be:
a) a 3
b) a score less than 4
c) an even number
2.
A letter is chosen from the word 'terrific'. Determine the probability that it will be:
a) an f
b) an r
c) a vowel
d) a consonant
3.
A bag contains 3 red balls, 5 blue balls and 2 green balls. A ball is chosen at
random from the bag. Find the probability that it will be:
a) green
b) blue
c) red
d) not red
4.
There are 7 tomatoes in a bag. Four of them are red and the remainder are green.
A tomato is picked at random from the bag. What is the probability that it is red?
5.
20 discs numbered 1 to 20 are placed in a box and one disc is chosen at
random. Determine the probability that the number on the disc will be:
a) even
b) a multiple of 3
c)
more than 8
d) less than 8
6.
A card is drawn from a deck of 52 playing cards. Find the probability that it will be:
a) the king of hearts
b) a queen
c) an ace, king, queen or jack
d) the jack of spades or the ace of diamonds
7.
Which of the following events is impossible:
a) drawing an ace from a deck of 52 playing cards
b) having a birthday on 32 July
c)
snow in June
d) rain tomorrow
Workbook 16
Level 1 Numeracy/Application of Number
4
© West Nottinghamshire College 2004
basic & keySKILLBUILDER
Handling Data
Probability
HD2/L1.2
We can show probability on a line.
0
1 or 100%
impossible
certain
Exercise 2
Draw a probability line and mark on the following events:
1.
a)
b)
c)
d)
e) – g)
You will climb Mount Everest
That the next bus you see is red
If you drop a weight it will fall
That a drawing pin will land point down
Choose 3 of your own and mark them.
2.
Express the above (a - g) as percentages.
a)
b)
c)
d)
e)
f)
g)
3.
Show b) and d) – g) as decimal fractions
b)
d)
e)
f)
g)
f)
g)
4.
Show b) and d) – g) as fractions
b)
Workbook 16
d)
e)
Level 1 Numeracy/Application of Number
5
© West Nottinghamshire College 2004