# Probability with marbles and no replacements

Two marbles are drawn randomly one after the other without replacement from a jar that contains 4 red marbles, 4 white marbles, and 7 yellow marbles. Find the probability of the following events:
(a) A red marble is drawn first followed by a white marble.
(b) A white marble is drawn first followed by a white marble.
(c) A yellow marble is not drawn at all.

I understand how to do this with replacements but don't understand how to adapt the formula to no replacements

• Welcome to the site. Please explain what you have tried. – N. F. Taussig Sep 26 '14 at 20:51
• I am lost. I understand how to do this with replacements but don't understand how to adapt the formula to no replacements – Amanda Sep 26 '14 at 21:38
• Without replacements, the # of marbles available for the 2nd draw would be 14 instead of 15. That is the difference between no replacements and replacements. – David Sep 26 '14 at 21:49
• Thank you so much! This was so much easier to understand than that book! – Amanda Sep 26 '14 at 22:02
• Your welcome. When thinking about simple probability, think in terms of # of good outcomes divided by total number of outcomes. I tried to answer this question as simply as I could so you could understand it easily. – David Sep 26 '14 at 22:21

red marble drawn first is $4/15$, white marble drawn next is $4/14$ so
a) $4/15$ * $4/14$ = $16/210$ = $8/105$
white marble drawn first is $4/15$, white marble drawn next is $3/14$ so
b) $4/15$ * $3/14$ = $12/210$ = $6/105$ = $2/35$
no yellow marble drawn is $8/15$ * $7/14$
c) = $8/15$ * $7/14$ = $56/210$ = $28/105$ = $4/15$