A bag B₁ has 3 white balls and 2 red balls. Another bag B₂ has 4 white and 6 red balls. A ball is drawn randomly from bag B₁ and with out seeing it’s colour, is being put in bag B₂. Now a ball is drawn from bag B₂. The probability of both the drawn balls, of being same colour, is

$\frac{29}{55}$

E₁ : Ball drawn from B₁ is white.

E₂ : Ball drawn from B₁ is red.

A : Both the drawn balls are of same colour.

$P(A)=P\left(E_1\right) . P\left(A / E_1\right)+P\left(E_2\right) . P\left(A / E_2\right)$

$=\frac{3}{5} . \frac{5}{11}+\frac{2}{5} . \frac{7}{11}=\frac{29}{55}$