Probability
Total Probability
IIT-JEE 1992
Grade 12
Question:
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour noted, and it is returned to the urn along with 2 more balls of the same colour. A ball is then drawn at random from the urn. The probability that the second ball drawn is red is:
(1) $\frac{7}{12}$
(2) $\frac{5}{12}$
(3) $\frac{1}{2}$
(4) $\frac{7}{24}$
Step-by-Step Solution
Key Concept: Use the law of total probability, conditioning on the colour of the first ball drawn — note how the composition of the urn changes before the second draw in each case.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)