Question

Urn 1 contains 5 red and 3 Blue marbles and Urn 2 contains 7 red marbles and 3 blue marbles. A marble is randomly selected from Urn 1 and Placed in Urn 2. A marble is then drawn from Urn 2 a. What is the probability that the marble drawn from Urn 2 is red? b. What is the conditional probability that the ball drawn from Urn 1 is red, given that a blue marble is drawn from Urn 2?

Answer 1

Explanation:

Urn 1

5 red, 3 blue

Urn 2

7 red, 3 blue

When a marble is selected at random from urn 1,

P(red) =
`(5)/(8) =0.625`

P(blue) =
`1-0.625\\=0.375`

When red is drawn p of drawing red from second urn =
`(8)/(11)`

Otherwise p of drawing red from second urn=
`(7)/(11)`

a) the probability that the marble drawn from Urn 2 is red

=
`(8)/(11) *(5)/(8) +(7)/(11) *(3)/(8) \\=(61)/(88)`

b) the conditional probability that the ball drawn from Urn 1 is red, given that a blue marble is drawn from Urn 2

= prob from urn 2/answer for a

=
`(21)/(88) /(61)/(88) \\=(21)/(61)`