Question

@triciaal @Directrix @zepdrix @mathmate
A sack of 10 balls has 1 red ball. I choose 3 balls. What is the probability that my 3 balls are not red?

Answer 1

i know this is a hyper-geometric distribution.
where
n = sample size
k=number of successes
N= population size
x = ....actually idk but I'm guessing trials? :o

\[P(X=x) = \frac{\left(\begin{matrix}k \\ x\end{matrix}\right)\left(\begin{matrix}N-k \\ n-x\end{matrix}\right)}{\left(\begin{matrix}N \\ n\end{matrix}\right)}\]

Answer 2

oh, apparently x = 1 since we need 1 red ball.

Answer 3

My stats knowledge is pretty rusty but isnt the probaboiity

9/10 * 8/9 * 7/8 ?

Answer 4

alternate view

Answer 5

@welshfella The answer is 0.271 btw. I don't think we're using the method u used.

Answer 6

Oh Ok - then my method is not correct

Answer 7

Fyi, this is what I thought:
\[P(X=x) = \frac{\left(\begin{matrix}1 \\ 1\end{matrix}\right)\left(\begin{matrix}9 \\ 2\end{matrix}\right)}{\left(\begin{matrix}10 \\ 3\end{matrix}\right)}\] Since that finds the probability of getting 1 red ball. (Which turns out to be 0.3)

Answer 8

and the complement would be...like welsh said..0.7 Triciaal if you get the same answer, i'll just ask my teacher on whether there was a mistake.