Create two questions which showcase the use of
addition rule and multiplication rule of probability
respectively when you have 04 sets, of 05 balls each,
with different colours, and solve them
Answers
Answer:
Addition and
Multiplication Laws
of Probability
✓
✒
✏
35.3✑
Introduction
When we require the probability of two events occurring simultaneously or the probability of one or
the other or both of two events occurring then we need probability laws to carry out the calculations.
For example, if a traffic management engineer looking at accident rates wishes to know the probability
that cyclists and motorcyclists are injured during a particular period in a city, he or she must take
into account the fact that a cyclist and a motorcyclist might collide. (Both events can happen
simultaneously.)
✛
✚
✘
✙
Prerequisites
Before starting this Section you should . . .
• understand the ideas of sets and subsets
• understand the concepts of probability and
✬
events
✫
✩
✪
Learning Outcomes
On completion you should be able to . . .
• state and use the addition law of probability
• define the term independent events
• state and use the multiplication law of
probability
• understand and explain the concept of
conditional probability
HELM (2008):
Section 35.3: Addition and Multiplication Laws of Probability
29The addition law
As we have already noted, the sample space S is the set of all possible outcomes of a given experiment.
Certain events A and B are subsets of S. In the previous Section we defined what was meant by
P(A), P(B) and their complements in the particular case in which the experiment had equally likely
outcomes.
Events, like sets, can be combined to produce new events.
• A ∪ B denotes the event that event A or event B (or both) occur when the experiment is
performed.
• A ∩ B denotes the event that both A and B occur together.
In this Section we obtain expressions for determining the probabilities of these combined events,
which are written P(A ∪ B) and P(A ∩ B) respectively.
Types of events
There are two types of events you will need to able to identify and work with: mutually exclusive
events and independent events. (We deal with independent events in subsection 3.)
Mutually exclusive events
Mutually exclusive events are events that by definition cannot happen together. For example, when
tossing a coin, the events ‘head’ and ‘tail’ are mutually exclusive; when testing a switch ‘operate’
and ‘fail’ are mutually exclusive; and when testing the tensile strength of a piece of wire, ‘hold’ and
‘snap’ are mutually exclusive. In such cases, the probability of both events occurring together must
be zero. Hence, using the usual set theory notation for events A and B, we may write:
P(A ∩ B) = 0, provided that A and B are mutually exclusive events
Task
Decide which of the following pairs of events (A and B) arising from the experi-
ments described are mutually exclusive.
(a) Two cards are drawn from a pack
A = {a red card is drawn}
B = {a picture card is drawn}
(b) The daily traffic accidents in Loughborough involving pedal cyclists and
motor cyclists are counted
A = {three motor cyclists are injured in collisions with cars}
B = {one pedal cyclist is injured when hit by a bus}
(c) A box contains 20 nuts. Some have a metric thread, some have a
British Standard Fine (BSF) thread and some have a British Standard
Whitworth (BSW) thread.
A = {first nut picked out of the box is BSF}
B = {second nut picked out of the box is metric }
30 HELM (2008):
Workbook 35: Sets and Probability