a bag contains 10 black and 16 white balls.22 balls are drawn one by one till 4 white balls remain in the bag.what is the probability the 22th ball drawn is black. all balls are distinct.

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- Dec 8th 2010, 06:54 AMayushdadhwalprobabilty
a bag contains 10 black and 16 white balls.22 balls are drawn one by one till 4 white balls remain in the bag.what is the probability the 22th ball drawn is black. all balls are distinct.

- Dec 9th 2010, 04:31 AMCaptainBlack
- Dec 9th 2010, 10:19 AMSoroban
Hello, ayushdadhwal!

Quote:

$\displaystyle \text{A bag contains 10 black and 16 white balls.}$

$\displaystyle \text{22 balls are drawn one by one untll 4 white balls remain in the bag.}$

$\displaystyle \text{What is the probability the 22th ball drawn is black.}$

$\displaystyle \text{All balls are distinct.}$ . Is this relevant?

I have a back-door approach to this problem.

I may be totally wrong, but I can't shake my reasoning.

. . . . . . . . . $\displaystyle \overbrace{\circ\;\bullet\;\bullet\;\circ\;\bullet \;\hdots\;\square}^{\text{10 black, 12 white}}\;|\;\circ\;\circ\;\circ\;\circ $

. . . . . . . . . . . . . . . . . . . . $\displaystyle \Uparrow$

What is the probability that**this**is black?

Isn't it .$\displaystyle \dfrac{10}{22} \:=\:\dfrac{5}{11}$ ?

- Jan 2nd 2011, 05:38 AMayushdadhwal
will someone explain soroban sir's answer

- Jan 2nd 2011, 05:57 AMCaptainBlack