Q12 of 43 Page 296

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?

Given that one urn contains two black balls and one white ball

and second urn contains one black ball and two white balls



It is also given that one of the two urns is chosen, then a ball is randomly chosen from the urn, then second ball is chosen at random from the same urn without replacing the first ball


(a) Sample Space S = {B1B2, B1W, B2W, B2B1, WB1, WB2, W1W2, W1B, W2B, W2W1, BW1, BW2}


Total number of sample space = 12


(b) If two black balls are chosen


Total outcomes = 12


Favourable outcomes are B1B2, B2B1


∴ Total favourable outcomes = 2


We know that,




(c) If two balls of opposite colours are chosen


Favourable outcomes are B1W, B2W, WB1, WB2, W1B, W2B, BW1, BW2


∴ Total favourable outcomes = 8


and Total outcomes = 12


We know that,




More from this chapter

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10

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).

 11

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.

 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

 14

If the letters of the word ASSASSINATION are arranged at random. Find the Probability that

(a) Four S’s come consecutively in the word


(b) Two I’s and two N’s come together


(c) All A’s are not coming together


(d) No two A’s are coming together.