Two events are said to be mutually exclusive, if they cannot both occur simultaneously.

The Venn diagram below represents the situation in which set A and B are mutually exclusive or disjoint

in this case p(A) = p(B) = p(AuB)

Addition Law

If events A, B,C … are mutually exclusive the probability of A or B or C or …. happening is the sum of their individual probabilities

i.e P(A) f p (b) +P (C) + ……………………..

Complementary events

Recall that E is the complement of the set

pr (Ec) = 1 – pr(E)

Ex. 1 A number is chosen at random from the set {2,4,6, … 20). Find the probability that it is either a factor of 18 or a multiple of S.

Solution

n(S) = 10

n(factor of 18) = 2,3,6,18,9

= 2,6,18

Therefore = n(factors of 18) =3

p( factor of 18) = 3/10

Multiple of 5 =5,10,15,20

n(multiple of 5) =2

in the set

p(multiple of 5) = 2/10

Independent Events

Two events are said to be independent if the two events have no effect on each other . For example the task of getting both a six and a tail in a throw

Ex 2: Five girls and three boys put their names in a box. One name is picked out at random without replacing the first name; a second name is picked out at random. What it the probability that both are names of girls?

Solution

p (picking a girl) = 5/8

P(picking another girl without replacement) = 4/7

pr (both are names of girls) =

Outcome tables , tree diagrams

Ex 4 A bag contains three black balls and two white ball. A ball is taken from the bag and then replace. A second ball is choose.

What is the probability that

- a) they are both white.
- b) one is black and one is white
- c) at least one is black
- d) at most is black

Solution

The possible ways of selecting the balls are shown on a tree diagram