Question 758780
<pre>
I calculated a probability that must be
incorrect. 
******* Here is the problem statement:
Given: You have 100 colored marbles in
a bag; 25-Red, 25-Blue, 25-Green & 
25-Yellow.
Problem: What is the probability of
drawing 4 marbles (at 1 time) of the
same color? 
******* Here is my solution:
There are 25-Red + 25-Blue + 25-Green +
25-Yellow = 100 total marbles.
Draw 4 marbles at a time. 
The possible outcomes = 100C4 = 825 
<font color="red">No! 100C4 = 3921225
</font>
The number of ways to draw 4-Red marbles out of 25 is 25C4 = 50. 
<font color="red">No! 25C4 = 12650
</font>
The number of ways to draw 4-Blue marbles out of 25 is 25C4 = 50. 
<font color="red">No! 25C4 = 12650
</font>
The number of ways to draw 4-Green marbles out of 25 is 25C4 = 50. 
<font color="red">No! 25C4 = 12650
</font>
The number of ways to draw 4-Yellow marbles out of 25 is 25C4 = 50. 
<font color="red">No! 25C4 = 12650
</font> 
The total ways you can get 4 of the same colored marbl
es is 50+50+50+50 = 200 
<font color="red">No! 12650+12650+12650+12650 = 50600
</font> 
P(ALL THE SAME COLOR) = 200 / 825 = 24%. 
<font color="red">No! 50600/3921225
 = 0.0129041307 = or about 1.29%

You are calculating combinations incorrectly.  If you have a TI-83 or 84,

To calculate 100C4,

Type 100
Press MATH
Press left arrow key once
Press 3
Type 4    read 100 nCr 4
Press ENTER     read 3921225
  
</font>
Edwin</pre>