Question

Assertion :There are two bags (i) & (ii), bag (i) contains 3 red & 4 black balls & bag (ii) contains 5 red & 6 black balls. If one ball is drawn at random from one of the bags and found to be red then the probability that it was drawn from bag(ii) is 35/68. Reason: If $E_1$, & $E_2$ events constitute a partition of sample space S & A is any event of non zero probability, then $P\left(E_i/A\right)=\frac{P\left(E_i\right)P\left(A/E_i\right)}{P\left(A\right)}$, $(i=1,2)$.

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion

Let $E_1=$ event of choosing bag (i) & $E_2$ the event of
choosing the bag (ii) & '$A$' be the event of drawing red ball
$\therefore P\left(E_1\right)=P\left(E_2\right)=\frac{1}{2}$
$\therefore P\left(A/E_1\right)=\frac{3}{7},P\left(A/E_2\right)=\frac{5}{7}$
$\therefore P\left(E_2/A\right)=\frac{P\left(E_2\right)P\left(A/E_2\right)}{P\left(A\right)}=\frac{\frac{1}{2}\times \frac{5}{11}}{\frac{1}{2}\times \frac{3}{7}+\frac{1}{2}\times \frac{5}{11}}=\frac{35}{68}$