148k views
1 vote
Box 1 contains 2 yellow and 4 green balls, whereas Box 2 contains 1 yellow and 1 green ball. A ball is randomly chosen from Box 1 and then transferred to Box 2, and a ball is then randomly selected from Box 2. a. What is the probability that the ball selected from Box 2 is yellow? b. What is the conditional probability that the transferred ball was yellow, given that a yellow ball is selected from Box 2?

User Jake Smith
by
8.4k points

1 Answer

3 votes

Answer:

Explanation:

Given

Box 1 contains 2 yellow and 4 green balls

box 2 contains 1 yellow and 1 green ball

case 1 when yellow ball is chosen and transferred to second box thus Probability associated with it


P_1=(2)/(6)* (2)/(3)=(4)/(18)

case 2 when Green ball is chosen and transferred to second box thus Probability associated with it


P_2=(4)/(6)* (1)/(3)=(4)/(18)

Thus Probability that ball selected form Box 2 is yellow


P=P_1+P_2=(4)/(18)+(4)/(18)=(8)/(18)

(b) P(transferred ball is yellow|Yellow ball is selected)


P(Yellow\ ball\ is\ selected)=(8)/(18)


P(transferred\ ball\ is\ yellow|Yellow\ ball\ is\ selected)=(Probability\ of\ transferring\ yellow\ ball)/(Probability\ of\ selecting\ Yellow\ ball)


P=((4)/(18))/((8)/(18))=0.5

User Aaron Taveras
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories