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An urn contains 5 red and 2 green balls....

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn, the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red is

A

`(27)/(49)`

B

`(26)/(49)`

C

`(21)/(49)`

D

`(32)/(49)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let A be the event that ball drawn is given and B be the event that ball drawn is red.
`:." "P(A)=(2)/(7)" and "P(B)=(5)/(7)`
Again, let C be the event that second ball drawn is red.
`:." "P(C)=P(A)P(C//A)+P(B)P(C//B)`
`=(2)/(7)xx(6)/(7)+(5)/(7)xx(4)/(7)`
`=(12+40)/(49)=(32)/(49)`
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