Here are the answers to the non-calculator probability questions: 1. 0.35 2. 0.25 3. 0.75 4. 0.1 5. 0.8 6. 0.15 7. 0.5 8. 0.987 9. 2 10. 1.98 11. 30 12. 1/36

1. WORKSHEET 1 – Probabilities - Mutually Exclusive Events
1. A card is picked at random from these number cards.
25 26 27 28 29 30 31 32 33 34 35 36
The event A is ‘The number picked is odd’.
The event B is ‘The number picked is a multiple of four’.
The event C is ‘The number picked is prime’.
The event D is ‘The number picked is a square number’.
The event E is ‘The number picked is even’.
(a) Work out the probability of each event.
(b) Tick () the pairs of events that are mutually exclusive.
A and B B and C A and D B and D C and E C and D D and E
(c) What is the probability that the number picked is:
(i) either odd or a multiple of 4?
(ii) either prime or a multiple of 4?
(iii) either prime or a square?
(iv) either even or prime?
Note : Two Events are MUTUALLY EXCLUSIVE when they cannot happen together.
Eg. You cannot have a number that is both ODD and EVEN
when Events A and B are mutually exclusive P ( A OR B ) = P(A) + P(B) .
2. A spinner is made of a circle, divided in 8 equal sectors, each
numbered as shown. A pointer is fixed to the centre and is
free to spin. A trial consists of spinning the pointer and noting
the number on which the pointer stops.
(a) Work out the probability of getting (i) a 5 or a 3
(ii) an even number
The pointer is spun twice and the two numbers noted.
(b) Work out the probability that the two numbers are
(iii) both even (iv) both a multiple of 4.
3. Amanda has two similar hexagon spinners, both numbered as shown.
She spins them both.
What is the probability that:
a) both spinners show 5.
b) the first spinner shows 5 and the second shows an even number.
c) both spinners show a multiple of 4.
d) both spinners show a prime or a square number
Note: For Two Events A and B, both happening P ( A AND B ) = P(A) × P(B) .
4. Karl takes a card at random from this pack and keeps it. Then he takes a second card
at random.
Find the probability that he takes one odd number and
one even number (in either order).
1 2 3 4 5

2. red
blue
blue
white
white
red
blue
blue
r
white
white
white
WORKSHEET 2 – Tree Diagrams - Independent Events
SPINNER A SPINNER B
1. Spinners A and B are spun together.
Spinner A Spinner B
Fill in the Tree Diagram above and use it to give the following probabilities :
(a) P(both blue)
(b) P(same colour)
(c) P(red and blue)
(d) P(spinner B shows red)
(e) P(spinner A shows white)
(f) P(at least one spinner shows red)
(g) P(only one spinner shows red)
2. A bag contains green and yellow balls and a second bag contains green, yellow and red
balls. A ball has to be picked from each bag.
The probability of picking a green ball from the
first bag is 0.4 and in the second bag there are
2 green balls, 5 red balls and 3 yellow ones.
Fill in a tree diagram to give the
following probabilities:
a) P(1st
yellow, then red ball)
b) P(no green ball)
c) P(balls of the same colour)
d) P(a yellow and a green ball)
e) P(at least one ball is yellow)
f) P(only one ball is yellow) 1st
Bag 2nd
Bag
P(Green) = 0.4
P(Green) =
P(Yellow) =
P(Red) =
P(Yellow) =

3. does not water
plant
waters
plant
flowers grow
flowers grow
flowers do not grow
flowers do not grow
3. Alfred calculates the probability that a person develops an allergy after taking some
medicines. For Medicine A this is
1
1000
. For Medicine B this is
3
10 000
.
a) Complete the probability tree.
Erika takes Medicine A and Medicine B.
b) What is the probability that she develops an allergy to both medicines?
c) Show that the probability that she develops an allergy to only one medicine is about
13
10 000
.
4. The probability that Lina waters her plant is
4
7
.
If she waters her plant, the probability that flowers grow is
3
5
.
If she does not water her plant, the probability that flowers grow is
3
5
.
i) Complete the tree diagram below:
ii) Calculate the probability that flowers grow.

4. WORKSHEET 3 – Tree Diagrams - Dependent Events
1. On my way to work, I pass 2 sets of traffic lights.
The probability that the first set is green is
3
4
.
If the first set is green, the probability that the second set is green is
2
3
.
If the first set is not green the probability that the second set is green is
3
5
.
a) Fill in the missing probabilities on the tree diagram.
b) What is the probability that :
i) both are green
ii) none is green
iii) exactly one is green
iv) at least one is green
First set Second set
2. James is taking a test consisting of two
papers.
The probability that he passes Paper I is 0.7.
If he passes Paper I the probability that he is
successful in Paper II is 0.6.
If he fails Paper I the probability that he is
successful in Paper II is 0.3.
(i) Complete the tree diagram
(ii) Use the probability tree to work out
the probability that James
a) will pass both papers
b) will pass at least one paper.
(iii) If James fails in only one paper he
is allowed to sit for it a second time.
What is the probability that James
will have to repeat one of the
papers?

5. 3.
A pack is made up of cards with numbers from 1 to 7.
Two cards are going to be drawn, without replacing the first one.
a) Complete the probability tree for odd and even numbers to be drawn.
b) What is the probability that both cards drawn show an odd number?
A third card is now going to be drawn (without replacing the first and second cards).
c) What is the probability that the three cards show an odd number?
4. The letters of the word PROBABILITY are written on eleven cards, one letter on each card.
The cards are shuffled and one card is chosen at random.
(i) Find the probability that the card chosen in B.
The experiment is repeated but this time two
cards are drawn.
The first card is not replaced after the first
card has been withdrawn.
(ii) Complete the probability tree.
(iii) Write down the probability that one
card is a vowel (V) and the other is a
consonant (C).

6. WORKSHEET 4 – Probabilities - Revision Questions
Non Calculator Question : Answers
1] In a bag there are only red discs and blue discs.
A disc is chosen at random. The probability that the disc is blue is 0.65.
What is the probability that the disk is red?
2] A match can be either won, lost or drawn. The probability that team A
wins a match is
7
2
. The probability that team A obtains a draw is
7
4
.
What is the probability that team A loses the match?
3] There are 4 yellow, 6 green and 8 blue marbles in a bag.
One marble is to be drawn.
What is the probability that it is not a green marble?
4] The following table shows
information about the eye colour
of a group of children.
What is the probability that a child chosen at random from this group is a
blue eyed boy?
Boys Girls
Blue Eyed 5 3
Brown Eyed 8 7
5] I throw a die numbered 1 to 6. What is the probability that I get a number
less than 5?
6] There are 20 pink pages, 15 green pages and 25 yellow pages in a book.
I open the book at random and choose a page.
What is the probability that I land on a green page?
7] What is the probability of obtaining a multiple of 3 when a fair dice is
tossed once?
8] The probability that it will rain tomorrow is 0.013.
What is the probability that it will not rain tomorrow?
9] Two hundred and forty tickets are sold in a raffle.
One ticket will be drawn to determine the prize winner.
Rita has 0.1 chance of winning the prize. How many tickets did Rita buy?
10] The probability that it will rain in Sunbrook on a given day in August is .
How many rainy days should you expect, if you go to Sunbrook for 14 days
in August?
11] A dice is rolled 180 times.
How many times would you expect to get a prime number?
12] What is the probability that if I roll two dice I get two sixes?