1.

Bag A contains 2 white and 3 red balls, and bag B contains 4 white and 5 red balls. One ball is drawn at randow from one of the bags and it is found to be red. Find the probability that it was drawn from bag B.

Answer»

SOLUTION :Let `E_1`= ENVENT of CHOOSING bag A,
`E_2`= event of choosing bag B, and
E= event of drawing a red ball.
Then, `P(E-1)=1/2 and P(E-2)=1/2`
Also, `P(E//E_1)`= event of drawing a red ball from bag `A=3/5`, and
`P(E//E-2)` = event of drawing a red ball from bag `B=5/9`.
Probability of drawing a ball from B, it being given that it is red `=P(E_2//E)`
`=(P(E//E_2).P(E_2))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2))`[by Bayes's theorem]
`=((5/9xx1/2))/((3/5xx1/2)+(5/9xx1/2))=25/52`.
Hence, the REQUIRED probability is`25/52`.


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