Q11 of 43 Page 296

The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P (A ∩ B) = .07. Determine


(a) P (A)


(b)


(c) P (A ∪ B)


(d) P (A ∩ B)


(e) P (B ∩ C)


(f) Probability of exactly one of the three occurs.

Given P(A ⋂ B) = 0.07

From the given Venn Diagram


(a) P(A)



P(A) = 0.13 + 0.7 = 0.20


(b)



= 0.07 + 0.10 + 0.15 – 0.15


= 0.07 + 0.10


= 0.17



(c) P(A ⋃ B)


By General Addition Rule,


P(A ⋃ B) = P(A) + P(B) – P(A ⋂ B)


⇒ P(A ⋃ B) = 0.20 + (0.07 + 0.10 + 0.15) – 0.07


⇒ P(A ⋃ B) = 0.20 + 0.25


⇒ P(A ⋃ B) = 0.45


(d)


We know that,



= 0.20 – 0.07 [from part (a)]


= 0.13


(e) P(B ⋂ C)



P(B ⋂ C) = 0.15


(f) Probability of exactly one of the three occurs



P(exactly one of the three occurs) = 0.13 + 0.10 + 0.28


= 0.51


More from this chapter

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9

Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is twice as likely to be selected as B, and B and C are given about the same chance of being selected, while C is twice as likely to be selected as D, what are the probabilities that

(a) C will be selected?


(b) A will not be selected?

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One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month. Consequently the sample space consists of four elementary outcomes S = {John promoted, Rita promoted, Aslam promoted, Gurpreet promoted} You are told that the chances of John’s promotion is same as that of Gurpreet, Rita’s chances of promotion are twice as likely as Johns. Aslam’s chances are four times that of John.

(a) Determine P (John promoted)


P (Rita promoted)


P (Aslam promoted)


P (Gurpreet promoted)


(b) If A = {John promoted or Gurpreet promoted}, find P (A).

 12

One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball.

(a) Write the sample space showing all possible outcomes


(b) What is the probability that two black balls are chosen?


(c) What is the probability that two balls of opposite colour are chosen?

 13

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that

(a) All the three balls are white


(b) All the three balls are red


(c) One ball is red and two balls are white