Question

Assume a jar has 7 red marbles and 3 black marbles. Draw out 3 marbles, with and without replacement. Find the requested probabilities.

a) P( 3 black marbles) with replacement, without replacement

b) P( 1 red marble and 2 black marbles) with replacement, without replacement.

c) P( red on the first draw and black on the second draw, and black on the third draw) with replacement, without replacement.

Answer 1

3 black marbles with replacement
\[\frac{3}{10}\times \frac{3}{10}\times \frac{3}{10}=\left(\frac{3}{10}\right)^3\]
without replacement
\[\frac{3}{10}\times \frac{2}{9}\times \frac{1}{8}\] others are similar

Answer 2

That same technique doesn't work with the others :(

Answer 3

I figured out "c"! But everything I try for "b" doesn't work...