Question

An urn contains 5 red balls and 6 blue balls. A ball is drawn. If the ball is red, it is kept out of the urn and an additional blue ball is added to the urn. Then, a second ball is drawn from the urn. If the ball is blue, then it is put back in the urn and an additional blue ball is added to the urn. Then a second ball is drawn from the urn.

If the second drawn ball is blue, what is the probability that the first drawn ball was blue?

Select one:

A.

0.421053

B.

0.108108

C.

0.310345

D.

0.204545

E.

0.804878

F.

0.649351

G.

0.52381

H.

0.769231

Answer 1

Answer :

G. 0.52381

If the second drawn ball is blue, what is the probability that the first drawn ball was blue?An urn contains 5 red balls and 6 blue balls. A ball is drawn. If the ball is red, it is kept out of the urn and an additional blue ball is added to the urn. Then, a second ball is drawn from the urn. If the ball is blue, then it is put back in the urn and an additional blue ball is added to the urn. Then a second ball is drawn from the urn.

Number of balls in the urn = 11

Number of red balls in the urn = 5

Number of blue balls in the urn = 6

R1 : Event of first ball drawn is red;

P(R1) = Number of red balls in the urn/Number of balls in the urn = 5/11

If the first ball is red ; it is kept out of the urn and an additional blue ball is added to the urn;

Now number of blue balls = 6+1 = 7

Number of red balls = 5-1=4

total number of balls in the urn = 11

B2 : Event of second ball drawn is blue

P(B2|R1) = Probability of second ball drawn is blue given that first ball drawn is red

= Number of blue balls in the urn/total number of balls = 7/11

P(B2|R1) = 7/11

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B1 : Event of first ball drawn is blue;

P(B1) = Number of blue balls in the urn/Number of balls in the urn = 6/11

If the first ball is blue ;  If the ball is blue, then it is put back in the urn and an additional blue ball is added to the urn

Now number of blue balls = 6+1 = 7

Number of red balls = 5

total number of balls in the urn = 12

B2 : Event of second ball drawn is blue

P(B2|B1) = Probability of second ball drawn is blue given that first ball drawn is blue

= Number of blue balls in the urn/total number of balls = 7/12

P(B2|B1) = 7/12

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If the second drawn ball is blue, Probability that the first drawn ball was blue = P(B1|B2)

P(B1)P(B2|B1) = (6/11)(7/12) = 7/22

P(R1)P(B2|R1) = (5/11)(7/11) = 35/121

P(B1)P(B2|B1)+P(R1)P(B2|R1) = 7/22 + 35/121 = (1617)/(22*121)

If the second drawn ball is blue, Probability that the first drawn ball was blue = 0.52381

Answer :

0.52381