Probability

[vu12]

I need help with this probability question.

"Suppose you mized together a thousand black marbles and a thousance white marbles, all the same size. And suppose that a teaspoon holds three marbles. If you dipped successive spoonfuls of (three) marbles fro mthe mixture, would you occasionally get a spoonful that was all black or all white? If so, what would be the chance ? What about a spoonful that comprimises 10 marbles?"

 

[arthur ohlsten]

black marbles=1000
white marbles=1000


total ways of getting 3 marbles= \(\displaystyle \binom{2000}{3}\)
total ways of gettig 3 white marbles= \(\displaystyle \binom{1000}{3}\)
\(\displaystyle P[3 white]= \frac{\frac{1000!}{3!997! }}{\frac{2000!}{3!1997!}}\)

\(\displaystyle P[3white]= \frac{1000! 3! 1997!}{3! 997! 2000!}\)

\(\displaystyle P[3 white]= \frac{1000\cdot 999\cdot 998}{2000\cdot 1999\cdot 1998}\)

\(\displaystyle P[3 white]= \frac{998}{2\cdot 1999\cdot 3}\)

\(\displaystyle P[3white]= \frac{499}{5997}\)

you can solve for a spoon that holds 10
Arthur