Question

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?

Answer 1

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`