SOLUTION: 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.

Question 758780: 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
The number of ways to draw 4-Red marbles out of 25 is 25C4 = 50.
The number of ways to draw 4-Blue marbles out of 25 is 25C4 = 50.
The number of ways to draw 4-Green marbles out of 25 is 25C4 = 50.
The number of ways to draw 4-Yellow marbles out of 25 is 25C4 = 50.
The total ways you can get 4 of the same colored marbles is 50+50+50+50 = 200
P(ALL THE SAME COLOR) = 200 / 825 = 24%
This can't be correct! Can you help me understand the error in my calculation?
On the other hand, if it's correct, could you explain why it is correct?
Obviously, I have no confidence in my answer.
Thank you.
Answer by Edwin McCravy(20081) (Show Source): You can put this solution on YOUR website!

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 
No! 100C4 = 3921225

The number of ways to draw 4-Red marbles out of 25 is 25C4 = 50. 
No! 25C4 = 12650

The number of ways to draw 4-Blue marbles out of 25 is 25C4 = 50. 
No! 25C4 = 12650

The number of ways to draw 4-Green marbles out of 25 is 25C4 = 50. 
No! 25C4 = 12650

The number of ways to draw 4-Yellow marbles out of 25 is 25C4 = 50. 
No! 25C4 = 12650
 
The total ways you can get 4 of the same colored marbl
es is 50+50+50+50 = 200 
No! 12650+12650+12650+12650 = 50600
 
P(ALL THE SAME COLOR) = 200 / 825 = 24%. 
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
  

Edwin

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