Question

Two bags contain 10 balls each. Every round, you choose with equal probability one of the 2 bags and pick out a ball. After a while, you choose an empty bag. What is the probability for the other bag to contain exactly 4 balls at that time?

a. 2.90%
b. 6.10%
c. 10.80%
d. 12.20%

Answer 1

Answer: b) 6.10%

Explanation:

to find the probability for the other bag to contain exactly 4 balls at that time;

is only possible if you have chosen a particular bag 10 times and other bag 6 times.

After that, once again at the 17th attempt

so the required probability = ¹⁶c₁₀ × (1/2¹⁰ × (1/2)⁶ × (1/2)

= 0.610

CONVERT TO PERCENT

0.610 × 100

= 6.10%