KVPY SX SB Exam 2016 Question Paper

Question : 18 of 120

Marks: +1, -0

A box contains b blue balls and r red balls. A ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue is -

$b/{r+b}$
$b^2/({r+b})^2$
${b+1}/{r+b+1}$
${b(b+1)}/{(r+b)(r+b+1)}$

Validate

Solution:

P(b_2) = P(b_1).P(b_2/b_1)

+P(R_1).P(b_2/R_1)

=b/{b+r}.{b+1}/{b+r+1}

+r/{b+r}.b/{b+r+1}

=b/{b+r}

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