Question 41145
A jar contains 13 black and 12 red marbles. 
<font color=green>If one marble is drawn at random, what is the probability that it is black?</font>

If two marbles are drawn randomly from the jar in section a., what is the probability that the first is red and the second is black if the marbles are drawn....
<font color=red>With replacement?</font>
<font color=blue>Without replacement?</font>
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<font color=green>The first one is easy, it is 13 (for there are 13 blacks) over the total, 13+12=25.  The answer to the first is 13/25, or 52%.</font>
<font color=red>The probability of drawing a red one first is 12/25 or .48 .  After that, since we are replacing the red one in the jar, the probability of getting a black one is 13/25.  The probability of one happening first then the other is 12/25*13/25, which equals 156/625, or 24.96%.</font>
<font color=blue>The probability of the same but no replacement has the same probability for 1 black one, 13/25.  Then, we still have 12 red ones, but out of <b>24</b> total.  The answer is thence 13/25*12/24.  Why is it 24 instead of 25?  Because we <i>don't</i> replace the marble we took.  12/24=.5 so the probability without replacement is .5(13/25), or 13/50, equaling 26%.</font>
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