Question

Urn 1 contains 8 red and 6 Blue marbles and Urn 2 contains 5 red marbles and 4 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

a)

probability that the marble drawn from Urn 2 is red=P(marble from urn 1 is red and marble from urn 2 is red)+P(marble from urn 1 is blue and marble from urn 2 is red)

=(8/14)*(6/10)+(6/14)*(5/10)=39/70

b)

P(blue marble from urn 2)=1-P(red marble from urn 2)=1-39/70=31/70

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

=P(marble from urn 1 is red and marble from urn 2 is blue)/P(blue marble frm urn 2)

=(8/14)*(4/10)/(31/70)=16/31