In a 15-piece batch there are 5 black balls and the 10 remaining balls are white. 3 balls are selected randomly. The batch is discarded if among the chosen ones at least one selected ball is white.
What is the probability of this?
I assume the random selection is based upon no replacements, as 3 balls are taken at one go.
Formula: $P(X=x) = C(n,x) p^x (1–p)^{n-x}$
The probability of selecting a white ball is given by $\tfrac{10}{15}$, hence $\tfrac{2}{3}$ should be white.
But how about the probability distribution for at least one single white ball selected out of 3?
Thanks to @lulu: $1 - (\tfrac{5}{15} * \tfrac{4}{14} * \tfrac{3}{13}$) or just $1 - \binom 53 \Big / \binom {15}3$
$\endgroup$ 8 Reset to default
