An urn contains one red ball and one blue ball. At each step, a ball is picked…
2026
An urn contains one red ball and one blue ball. At each step, a ball is picked uniformly at random from the urn, and this ball together with another ball of the same color is put back in the urn. The probability that there are equal number of red and blue balls after two steps is
- A.
1/4
- B.
1/3
- C.
1/2
- D.
2/3
Attempted by 8 students.
Show answer & explanation
Correct answer: B
Initially, the urn contains 1 red ball and 1 blue ball (total 2).
After Step 1, picking either color (probability 1/2 each) changes the composition. If Red is picked first, the urn has 2R and 1B (total 3). If Blue is picked first, the urn has 1R and 2B (total 3).
To have equal numbers (2R, 2B) after Step 2, we need the opposite color in the second step. From (2R, 1B), picking Blue has probability 1/3. From (1R, 2B), picking Red has probability 1/3.
Total probability = (1/2 * 1/3) + (1/2 * 1/3) = 1/6 + 1/6 = 1/3.
A video solution is available for this question — log in and enroll to watch it.