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Chapter 3: Q.3.9 (page 98)

Consider3urns. An urn Acontains2white and 4red balls, an urn Bcontains 8white and 4 red balls and urn Ccontains 1white and 3red balls. If 1ball is selected from each urn, what is the probability that the ball chosen from urn Awas white given that exactly 2white balls were selected?

Short Answer

Expert verified

0.636365is the probability that the ball chosen from urn A was white given that exactly two white balls were selected.

Step by step solution

01

Step 1:Given Information

Given that 3urns. An urn localid="1647625690012" Acontains 2 white and 4 red balls, an urn Bcontains eight white and four red balls, and an urn Ccontains one white and three red balls.

02

Step 2:Explanation

Let Xbe the possibility that exactly two White balls are selected i.e.,(W,W,R)localid="1647625926749" (W,R,W)(R,W,W)

p(x)=26脳812脳34+26脳412脳14+46脳812脳14

Let Ybe the possibility that the first ball is white i.e.,(W,W,R)(W,R,W)

p(y)=26脳812脳34+26脳412脳14

p(y鈭�x)=26脳812脳34+26脳412脳1426脳812脳34+26脳412脳14+46脳812脳14

=0.1944440.305555

=0.636365

03

Step 3:Final Answer

If one ball is selected from each urn, 0.636365is the probability that the ball chosen from urn localid="1647625714756" Awas white given that exactly two white balls were selected.

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Most popular questions from this chapter

There is a 50鈥�50 chance that the queen carries the gene for hemophilia. If she is a carrier, then each prince has a 50鈥�50 chance of having hemophilia. If the queen has had three princes without the disease, what is the probability that the queen is a carrier? If there is the fourth prince, what is the probability that he will have hemophilia?

Let S = {1, 2, . . . , n} and suppose that A and B are, independently, equally likely to be any of the 2n subsets (including the null set and S itself) of S.

(a) Show that

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Hint: Let N(B) denote the number of elements in B. Use

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Show that P{AB = 脴} =34n

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