An urn contains 4 black balls and 6 white balls. What is the probability of getting 1 black ball and 1 white ball in two consecutive draws from the urn?
I know this is supposed to be easy. So i tried
(4/10) * (6/9) = 0.26667
But the correct answer is 0.53... which is *2 of that. Any hint why?
Because the order doesn't matter: you could also draw the white ball first, then the black ball: $$ \frac{4}{10} \cdot \frac{6}{9} + \frac{6}{10} \cdot \frac{4}{9} = \frac{8}{15} $$ If you know a little bit of combinatorics, we could also solve this problem by counting via combinations: $$ \frac{\binom{4}{1} \binom{6}{1}}{\binom{10}{2}} = \frac{8}{15} $$