# Ii none is black iii at least one is white 310

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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).