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)=26×812×34+26×412×14+46×812×14

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

p(y)=26×812×34+26×412×14

p(yx)=26×812×34+26×412×1426×812×34+26×412×14+46×812×14

=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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Example 5e, what is the conditional probability that the ith coin was selected given that the first n trials all result in heads?

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

P{A B} =34n

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

P{A B} =i=0nP{A (B|N(B) = i}P{N(B) = i}

Show that P{AB = Ø} =34n

A high school student is anxiously waiting to receive mail telling her whether she has been accepted to a certain college. She estimates that the conditional probabilities of receiving notification on each day of next week, given that she is accepted and that she is rejected, are as follows:

DayP(mail/accepted)P(mail/rejected)
Monday.15
.05
Tuesday.20
.10
Wednesday.25
.10
Thursday.15
.15
Friday.10
.20

She estimates that her probability of being accepted is .6.

(a) What is the probability that she receives mail on Monday?

(b) What is the conditional probability that she receives mail on Tuesday given that she does not receive mail on Monday?

(c) If there is no mail through Wednesday, what is the conditional probability that she will be accepted?

(d) What is the conditional probability that she will be accepted if mail comes on Thursday?

(e) What is the conditional probability that she will be accepted if no mail arrives that week?

Prove that if E1,E2,,Enare independent events, then

PE1E2En=1-i=1n1-PEi

Prove or give a counterexample. If E1 and E2 are independent, then they are conditionally independent given F.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free