Question

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

• A. $\frac{1}{2}$
• B. $\frac{4}{9}$
• C. $$\frac{5}{9}$$
• D. $$\frac{6}{9}$$

Answer 1

The correct option is A $\frac{1}{2}$

5 Red balls and 5 Black balls.
One ball discarded in first draw


From the above tree diagram, we get the probability of favourable branches (getting Red ball in second attempt) as;

Req. Prob. = (R in Ist and R in IInd) or (B in Ist and R in IInd)

$=(\frac{1}{2}\times \frac{4}{9})+(\frac{1}{2}\times \frac{5}{9})$

$=\frac{4}{18}+\frac{5}{18}=\frac{1}{2}$