Q.3.9 Consider3urns. An urn A聽contain... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 3: Q.3.9 (page 98)

Consider $3$ urns. An urn $A$ contains $2$ white and $4$ red balls, an urn $B$ contains $8$ white and 4 red balls and urn $C$ contains $1$ white and $3$ red balls. If $1$ ball is selected from each urn, what is the probability that the ball chosen from urn $A$ was white given that exactly $2$ white balls were selected?

Short Answer

Expert verified

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

Step by step solution

Step 1:Given Information

Given that $3$ urns. An urn localid="1647625690012" $A$ contains 2 white and 4 red balls, an urn $B$ contains eight white and four red balls, and an urn $C$ contains one white and three red balls.

Step 2:Explanation

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

$p (x) = \frac{2}{6} 脳 \frac{8}{12} 脳 \frac{3}{4} + \frac{2}{6} 脳 \frac{4}{12} 脳 \frac{1}{4} + \frac{4}{6} 脳 \frac{8}{12} 脳 \frac{1}{4}$

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

$p (y) = \frac{2}{6} 脳 \frac{8}{12} 脳 \frac{3}{4} + \frac{2}{6} 脳 \frac{4}{12} 脳 \frac{1}{4}$

$p (y 鈭� x) = \frac{\frac{2}{6} 脳 \frac{8}{12} 脳 \frac{3}{4} + \frac{2}{6} 脳 \frac{4}{12} 脳 \frac{1}{4}}{\frac{2}{6} 脳 \frac{8}{12} 脳 \frac{3}{4} + \frac{2}{6} 脳 \frac{4}{12} 脳 \frac{1}{4} + \frac{4}{6} 脳 \frac{8}{12} 脳 \frac{1}{4}}$

$= \frac{0.194444}{0.305555}$

$= 0.636365$

Step 3:Final Answer

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

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91影视

Short Answer

Step by step solution

Step 1:Given Information

Step 2:Explanation

Step 3:Final Answer

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91影视

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

Step by step solution

Step 1:Given Information

Step 2:Explanation

Step 3:Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.