Question

A urn contains 5 red and 5 black balls.A ball is drawn at random,its colour is noted and is returned to the urn.Morever,2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random.What is the probability that the second ball is red?

Answer 1

The correct answer is: \(\frac{1}{2}\)
The urn contains 5 red and 5 black balls. 
Let a red ball be drawn in the first attempt.
P (drawing a red ball)\(=\frac{5}{10}=\frac{1}{2}\)
If two red balls are added to the urn, then the urn contains 7 red and 5 black balls.
P (drawing a red ball)\(=\frac{7}{12}\)
Let a black ball be drawn in the first attempt
P (drawing a black ball in the first attempt)\(=\frac{5}{10}=\frac{1}{2}\)
If two black balls are added to the urn, then the urn contains 5 red and 7 black balls. 
P (drawing a red ball)\(=\frac{5}{12}\)
Therefore, probability of drawing second ball as red is
\(\frac{1}{2}\times \frac{7}{12}+\frac{1}{2}\times \frac{5}{12}=\frac{1}{2}(\frac{7}{12}+\frac{5}{12})=\frac{1}{2}\times 1=\frac{1}{2}\)