The Wey Valley School & Sports College
Mathematics Home Study
UNIT: Probability
Support work:
Page 1
Core work:
Page 2
Extension work: Page 3
(As a minimum you should be
completing one of these pages
preferably two)
Page 1
1. The following probability line shows the probabilities of 6
events, A, B, C, D, E, F
a) Which event is certain to occur?
b) Which event is the most unlikely to occur (but not
impossible)?
c) Which event is impossible?
d) Which events are more likely to occur than C?
A
REMEMBER
 Probability is on a scale of 0 to 1
 If something is impossible it has a probability of 0
 If it is certain to happen it has a probability of 1
 If it has an even chance of happening it has a probability of ½
To calculate the probability of an event happening you need to
list all the possible outcomes. This becomes the denominator
(bottom number) of your fraction. You then find how many of
these are the event you are interested in and this becomes the
numerator (top number) of your fraction.
Example 1: You have 3 red, 2 yellow, and 4 green disks.
What is the probability you pick a red one?
Answer: Total number of discs is 9, of which 3 are red; so 3  1 .
9
C
D
0
1
2. In a game you are given one of the following cards at random
1
2
3
4
5
6
7
a)
Are you more likely to be given an odd number or an
even number ?
b) Are you more likely to be given a 7 than a 5?
c) Are you more likely to be given a number greater or less
than 5?
H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6.
3. You flip a coin and spin a 4 sided spinner coloured red, green,
yellow and blue.
a) List all the possible outcomes
b) What is the probability of getting red and a head?
Page 3
1. A sweet jar contains 10 toffees, 8 mints and 12 chocolates.
A sweet is taken at random from the jar.
What is the probability that the sweet is:
1. An unbiased coin is tossed three times
a mint
a toffee
a chocolate
a mint or a toffee
not a mint
a chocolate or a toffee?
2. Jane rolls a fair six-sided die 300 times. How many times
would she expect to obtain:
a)
b)
c)
d)
e)
F
0.5
Page 2
a)
b)
c)
d)
e)
f)
E
3
Example 2: You have a coin and a die. List all the outcomes.
Answer:
B
a6
an even number
a number greater than 1
a number less than 3
a 2 or a 5?
3. Two fair dice have faces numbered 1 – 6.
a) Draw a table to show all the possible outcomes when the
two dice are rolled together and the two scores added
together to give a total score.
b) Calculate the probability that the total score is:
i) 7
ii) greater than 5
iii) an even number
iv) less than 4 v) a multiple of 4
vi) 1
a) List all the possible outcomes.
b) What is the probability of obtaining at least 2 heads?
c) What is the probability that all three tosses are the same?
2. A spinner has equal sections coloured Red (R), Purple (P),
Yellow (Y), Silver (S) and Black (B). The spinner is spun
twice and the colour it lands on noted.
a) List all the possible outcomes.
b) What is the probability that you obtain:
i) 2 reds
ii) the same colour for both spins
iii) a yellow and a red in any order
iv) no yellows?
3. In a game a card is taken at random from a full pack of 52
cards. It is then replaced, and a second card is taken.
Use a tree diagram to calculate the probabilities that:
a)
b)
c)
d)
both cards are diamonds
neither card is a diamond
one of the cards is a diamond
at least one card is a diamond