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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

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  • $\begingroup$ Welcome to the site. Please explain what you have tried. $\endgroup$ – N. F. Taussig Sep 26 '14 at 20:51
  • $\begingroup$ I am lost. I understand how to do this with replacements but don't understand how to adapt the formula to no replacements $\endgroup$ – Amanda Sep 26 '14 at 21:38
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    $\begingroup$ 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. $\endgroup$ – David Sep 26 '14 at 21:49
  • $\begingroup$ Thank you so much! This was so much easier to understand than that book! $\endgroup$ – Amanda Sep 26 '14 at 22:02
  • $\begingroup$ 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. $\endgroup$ – David Sep 26 '14 at 22:21
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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) = $8/15$ * $7/14$ = $56/210$ = $28/105$ = $4/15$

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