Probability and Combinations.

[mikemarachov]

A box contains 10 black balls and 10 white balls. We are choosing a ball, if it is white we take it out, if it’s black we put it back in. What is the probability that after 20 attempts we will take out all white balls.



I tried to accomplish this problem all weekend, Unfortunately no result.

Thanx for HELP!

Mike.

 

[tkhunny]

Rules of thumb:

1) Don't always try to tackle the WHOLE problem at the same time. Simplify your life.
2) Dive in. Don't be afraid of it.

Suppose there are 2 balls, one white and one black. Same rules. What is the probability that the white will be gone after 2 draws.

Draw 1 - White (1/2), [Black (1/2), Put it back and draw agaIn.]
Draw 2 - (1/2 - Only drawing the black on will get us here.) - White (1/2), Done, Black (1/2) Done.

Recap:

p(got the white on on the first draw) = 1/2
p(got the white on on the second draw) = p(black on first)*p(white on second) = (1/2)*(1/2)
p(both black) = (1/2)*(1/2)

Okay, this is actually looking awfully Negative Binomial! Ineresting conjecture to take into teh next attempt.

Suppose there are 4 balls, two white and two black. Same rules. What is the probability that the white balls will be gone after 4 draws.

Let's see what you get.