mathematics lesson 13, Lecture notes of Mathematics

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Independent

And

Dependent Events

Lesson no. 10

PROBABILITY of DEPENDENT and INDEPENDENT EVENTS Independent Events Two events may happen at the same time or one after the other. Two events are independent if the occurrence of that of the first event does not affect that of the second If events A and B are independent events in a sample space S, then the probability that both A and B occur is P(A and B) = P(A  B) = P(A) P(B)

Example: A bag contains 4 blue, 3 white and 5 red marbles. Two marbles are drawn at random with replacement. Find the probability that the first ball is red then the second is blue. Solution: P(red and blue) = P(red) • P(blue) = 5 12

4 12

5 12

1 3

5 36 Independent Event

Example: A bag contains 4 blue, 3 white and 5 red marbles. Two marbles are drawn at random without replacement. Find the probability that the first ball is red then the second is blue. Solution: P(red and blue) = P(red) • P(blue after red) = 5 12

• 4 11 = 5 12

4 11 = 20 132

5 33 Dependent Event

Example: You randomly select two cards from a standard 52- card deck. What is the probability that the first card is not a face card and the second card is a face card if: a. You do not replace the first card? Solution: P(non-face and face card) = P(non-face) • P(fc/nfc) = 40 52

• 12 51 = 10 13

12 51 = 120 663

40 221 Dependent Event

Example: A bag contains 4 blue balls and 6 red balls, two balls are taken at random, one after the other, with replacement. What is the probability of getting a blue on the first and red on the second draw Solution: P(blue balls and red balls) = P(blue) • P(red) = 4 10

6 10

24 ÷ 4 100 ÷ 4

6 25 Independent Event