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A bag contains 4 red and 6 blach balls O...

A bag contains 4 red and 6 blach balls O balls is drawn at random from the bag, its colour is observed and this ball along with two addibonal balls of the same colour are returnted to the bag, then the probabilaty then the drawn ball is red, is

A

`(3)/(10)`

B

`(2)/(5)`

C

`(1)/(5)`

D

`(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Key idea Use the theorem of total probability
Let `E_(1)=" Event that first ball drawn is red"`
`E_(2)=" Event that first ball drawn in black"`
`A=" Event that second ball drawn is rod"`
`P(E_(1))=(4)/(10),P((A)/(E_(1)))=(6)/(12)`
`implies" "P(E_(2))=(6)/(10),P((A)/(E_(2)))=(4)/(12)`
By law of total probability
`P(A)=P(E_(1))xxP((A)/(E_(1)))+P(E_(2))xxP((A)/(E_(2)))`
`=(4)/(10)xx(6)/(12)+(6)/(10)xx(4)/(12)=(24+24)/(120)=(48)/(120)=(2)/(5)`
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