2.  evaluate probabilities in simple cases by means of
enumeration of equiprobable elementary events (e.g.
for the total score when two fair dice are thrown), or by
calculation using permutations or combinations;
 use addition and multiplication of probabilities, as
appropriate, in simple cases;
 understand the meaning of exclusive and independent
events, and calculate and use conditional probabilities
in simple cases, e.g. situations that can be represented
by means of a tree diagram.

3. Sample Space
 It is the list of all possible outcome in an experiment.

4. ..
 Choosing a card from a standard pack of playing cards.
 The combined experiment of tossing a coin and a dice.
 Tossing a drawing pin on to a table to see whether it
lands point down or point up.

5.  A fair no-sided dice has eight faces colored red, ten
colored blue and two colored green. Then dice is
rolled.
A) Find the probability that the bottom face is red.
B) Let A be the event that the bottom face is not red.
Find the probability of A.

6. Activity 1
Using 2 dice, make a game that has 50 – 50 chances of
winning and losing.

7.  The number 1, 2, …, 9 are written on separate cards.
The cards are shuffled and the top one is turned over.
Calculate the probability that the number on this card
is prime.

8.  A circular wheel is divided into three equal sectors,
numbered 1, 2 and 3. The wheel is spun twice. Each
time, the score is the number to which the black arrow
points. Calculate the probabilities of the following
a) Booth score is the same.
b) Neither score is a 2.
c) At least one of the score is a 2
d) Neither score is a 2 and both scores are the same,
e) Neither the score is a 2 or both scores are the same.

9. Jafar has three playing cards, two queens and a king.
Tandi selects one of the cards at random, and returns
it to Jafar, who shufffles the cards. Tandi then selects a
second card. Tandi wins if both cards selected are
kings. Find the probability that Tandi wins?

10.  A dice with six faces has been been made from brass
and aluminum and is not fair. The probability of
getting 6 is ¼, the probabilities of 2, 3, 4, and 5 are
each 1/6, and the probability of 1 is 1/12. The dice is
rolled. Find the probability of rolling
a) A 1 or 6.
b) An even number.

11. You draw two cards from an ordinary pack. Find the
probability that they are not both kings?

12. Two pair dice are thrown. A price is won if the total is 10
or if each individual score is over 4. Find the
probability that a prize is won?

13.  Weather records indicate that the probability that a
particular day is dry is 3/10. Arid F.C. is a football team
whose record of success is better on dry days than on
wet days. The probability that Arid win on a dry day is
3/8, whereas the probability that they win on a wet day
is 3/11. Arid are due to play their next match on
Saturday.
a) What is the probability that Arid will win?
b) Three Saturdays ago Arid won their match. What is
the probability that it was a dry day?

14. Conditional Probability
 A conditional probability refers to the probability of
an event A occurring, given that another event B has
occurred.
 Notation: P(A B)
 Read this as the “conditional probability of A given B”
or the “probability of A given B.“
 These are especially useful in economic analysis
because probabilities of an event differ, depending on
other events occurring.

15. Formulae for conditional probabilities
 The probability of A given B is
P( A B)
P( A B)
P( B)
 The probability of B given A is
P( A B)
P ( B A)
P ( A)

16.  In a carnival game, a contestant has to first spin a fair
coin and then roll a fair cubical dice whose faces are
numbered 1 to 6. The contestant wins a prize if the
coin shows heads and the dice score is below 3. Find
the probability that a contestant wins a prize?

17.  A fair of cubical dice with faces numbered 1 t0 6 is
thrown four times. Find the probability that three of
the four throws result in a 6.

18. The Special Multiplication Rule (for independent events)
If events A, B, C, . . . are independent, then
P(A&B & C & ) = P(A) P(B) P(C)
What is the probability of all of these events occurring:
1. Flip a coin and get a head
2. Draw a card and get an ace
3. Throw a die and get a 1
P(A&B & C ) = P(A) · P(B) · P(C) = 1/2 X 1/13 X 1/6

19. Exercise 4B, numbers 1 -5