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2015-11-08T19:52:34+05:30

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3 red  balls        7  white balls.

P(Red) = 3/10                P(White) = 7/10

As the first marble drawn is put back in the bag,  probabilities remain same for the second marble drawn from the bag.  Both events of drawing of marbles are independent of each other.

Probability that both marbles are Red
   = P(first marble = Red  AND  2nd marble = Red)
   = 3/10 * 3/10 = 0.09

Probability that both are white
  = P(1st marble = White  AND 2nd marble = White)
  = 7 /10 * 7/10 = 0.49

Probability that both marbles drawn are of same color
  = 0.09 + 0.49 = 0.58

Given that both marbles are of the same color.  Then probability that both happened to be white =  0.49 / 0.58 = 0.845.
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We get this by applying the conditional probability theorem.

  P (B | A) =  P( B Π A ) / P(A)

 Here event B = both marbles are White.
                 A = both marbles are  of same color.
                 B Π A = both marbles are White = B

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