# A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, itscolour is observed and this ball along with two additional balls of the same colour arereturned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is : Option 1) $\frac{3}{4}$ Option 2) $\frac{3}{10}$ Option 3) $\frac{2}{5}$ Option 4) $\frac{1}{5}$

H Himanshu

P(R)$= 4/10\cdot 6/12+ 6/10\cdot 4/12=2/5$

Multiplication Theorem of Probability -

If A and B are any two events then

$\dpi{100} P\left ( A\cap B \right )= P\left ( B \right )\cdot P\left ( \frac{A}{B} \right )$

- wherein

where $\dpi{100} B\neq \phi$

Option 1)

$\frac{3}{4}$

Option 2)

$\frac{3}{10}$

Option 3)

$\frac{2}{5}$

Option 4)

$\frac{1}{5}$

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