Ball Paradox

Probability Level 2

A box initially contains a ball, which has a 50:50 chance of being black or white.

Then you put a white ball into the box, and randomly pick one ball out, which turns out to be a white ball.

What is the probability that the initial ball was white?

Note: This problem was stated by the famous author, Lewis Carroll (Charles Dodgson).

\dfrac{1}{4}

\dfrac{1}{3}

\dfrac{1}{2}

\dfrac{2}{3}

\dfrac{3}{4}

1