A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random

A box contains 3 yellow balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
A.1/4
B.1/2
C.5/8
D.2/3
E.3/4 





Yes, P(B) on any given pick = P(B) on the first pick.

An easier example:

Say we have 3 red marbles and 2 blue. What's the probability that the second marble picked is blue?

P(B) on the first pick is 2/5.

To get blue on the second pick, our two picks could be RB or BB:

P(R and B) = 3/5 * 2/4 = 3/10.

P(B and B) = 2/5 * 1/4 = 1/10.

Since either is a good outcome, we add the fractions:

3/10 + 1/10 = 4/10 = 2/5.

The same probability as getting blue on the first pick.

Pretty neat!



*****This is so because each ball is equally likely to be the fourth one (or nth one) drawn