In the basket there are white and black balls. Among them there are 4 white ones.

In the basket there are white and black balls. Among them there are 4 white ones. The message that the white ball was taken carries 3 bits of information. How many balls are there in the basket?

1. Let’s express the total number of balls in the basket through “x”.

2. Let’s calculate the probability of getting the white ball out of the basket: p = 4 / x.

3. Since the message that the white ball was taken carries 3 bits of information, applying the Hartley formula we get: log2 (1 / p) = 3, log2 (x / 4) = 3. It follows that x / 4 = 8, and x = 32.

Answer: There are 32 balls in the basket.