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Chapter 3: Q. 3.23 (page 99)

Urn Icontains 2white and 4red balls, whereas urn Πcontains 1white and 1red ball. A ball is randomly chosen from urn Iand put into urn II, and a ball is then randomly selected from urn Π. What is

(a) the probability that the ball selected from urn Πis white?

(b) the conditional probability that the transferred ball was white given that a white ball is selected from urn Π?

Short Answer

Expert verified

a) The probability that the ball selected White is 49

b) The probability that the transferred White ball was12

Step by step solution

01

 Set an occurrence  

When a white ball is chosen out from pot iandRithen be an occasion wherein a red ball is picked as from vase i,i∈[1,2]

02

Probability (part a)

a)

PW2=PW2∣W1PW1+PW2∣R1PR1=23×26+13×46=49
03

Chance (part b)

b)PW1∣W2=PW2∣W1PW1PW2=23×2649=12

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Most popular questions from this chapter

Show that if P(A)>0, then

P(AB∣A)≥P(AB∣A∪B)

There is a 60percent chance that event Awill occur. If Adoes not occur, then there is a 10percent chance that Bwill occur. What is the probability that at least one of the events AorBwill occur?

Repeat Problem 3.84 when each of the 3 players

selects from his own urn. That is, suppose that there are

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Consider an unending sequence of independent trials, where each trial is equally likely to result in any of the outcomes 1,2or3,. Given that outcome 3is the last of the three outcomes to occur, find the conditional probability that

(a) the first trial results in outcome 1;

(b) the first two trials both result in outcome 1.
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