Five marbles are randomly selected, one at a time (without return), from a bowl of 100 marbles (20 green, 30 blue, 10 yellow, and 40 black). What is the probability that all five marbles are black? (Answer in lowest terms).  Choose the correct choice from the following:
A) 201/125 B) 9139/1045660 C) 11350/146790 D) 21/75 E) 2/5
Let K = black. The bowl has 40 black marbles (we don't care what color the other marbles are because success is black only), so the probability of getting black is P(K) = 40/100 on the first selected marble.   Because selection is (without return), the P(K) has changed for following selections. Now, there are 99 marbles and black is dependent upon whether first marble was black, or not... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is:   Formula = P(A\B) = P(A and B)/P(B).   P(A\9139/1045660) = (40/100)(39/99)(38/98)(37/97)(36/96) = 78960960/9034502400 = 9139/1045660   Answer: 9139/1045660
<result>B</result>
Five marbles are randomly selected, one at a time (without return), from a bowl of 100 marbles (20 green, 30 blue, 10 yellow, and 40 black). What is the probability that all five marbles are black? (Answer in lowest terms).