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One ball left in the box

One ball left in the box

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%