ii.
none is black.
iii.
at least one is white.
3.10. REFERENCE BOOKS
1)
Agarwal, B.L.
‘Basic Statistics’,
Wiley Eastern Ltd., New Delhi.
2)
Gupta, S.P.,
’Statistics Methods’,
Sultan Chand and Co., New Delhi
3)
Levin, R., ‘Statistics
for Management’,
Prentice
–
Hall of India, New Delhi,
1984.
4)
Reddy, C.R.,
‘Quantitative Methods for Management Decision’,
Himalaya
Publishing House, Bombay, 1990.
3.11. LEARNING ACTIVITIES
A bag contains 8 red and 5 white balls. Two successive drawing of 3 balls are
made such that (i) balls are replaced before the second trial, (ii) balls are not
replaced before the second trial. Find the probability that the first drawing will give
3 white and the second 3 red balls.
3.12. KEY WORDS
Addition Theorems of Probability.
Multiplication Theorem of Probability.

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20
LESSON
–
4
CONDITIONAL PROBABILITY
4.1. INTRODUCTION
If the two events A and B are dependent, the above rule does not hold good. If
the events are dependent, the probability of the second event occurring will be
affected by the outcome of the first that has already occurred. The term conditional
probability is used to describe this situation. It is symbolically denoted by P (B/A).
This is read as the probability of occurring B, given A, has already occurred. Robert
L. Birte is defined the concept, condit
ional probability as: “A conditional probability
indicates that the probability that an event will occur is subject to the condition
that another event has already occurred.
Symbolically:
)
A
(
P
)
AB
(
P
A
B
P
)
B
(
P
)
AB
(
P
B
A
P
In conditional probabilities, the rule of multiplication in its modified form is:
P (A and B)= P (A)
P
A
B
P (A and B)
= P (B)
P
B
A
4.2 OBJECTIVES
The main aim of this Lesson is to study the Basics of conditional probability.
After going through this Lesson you should be able to:
1.
Understand the meaning of Conditional probability
2.
Baye’s Rule
4.3 CONTENTS
4.3.1. Conditional Probability
4.3.1.
Baye’s Rule
4.3.2. Illustrations
4.3.1. Conditional Probability
The
conditional probability
of an event
B
is the probability that the event
will occur given the knowledge that an event
A
has already occurred. This
probability is written
P(B|A)
, notation for the
probability of B given A
. In the case
where events
A
and
B
are
independent
(where event
A
has no effect on the
probability of event
B
), the conditional probability of event
B
given event
A
is simply
the probability of event
B
, that is
P(B)
.
If events
A
and
B
are not independent, then the probability of the
intersection
of
A
and
B
(the probability that both events occur) is defined by
P(A and B) = P(A)P(B|A).