We have a box inside which there is a ball that can be white or black but we don't know what color it is. Now we introduce a white ball into the box, shake it and extract a random ball that turns out to be white.

**What is the probability that the ball left in the box is black?**

#### Solution

At the moment when the two balls are in the box we have the following possible combinations with equal probability:

Scenario 1 with probability 1/2: Blanca1-Blanca2

Scenario 2 with probability 1/2: Black-White1

Now, from the two previous scenarios we extract a ball that we know is white.

If we are in the first scenario, we have zero chances of getting a black ball in the box because there is none.

If we analyze scenario 2, we have a 100% chance of a black ball remaining in the box since we have removed the White ball1.

Since both scenarios are equiprobable, we have to **the probability of a black ball remaining is (0 + 100) / 2 = 50%**