I just pulled three M&Ms from a bag that were all orange, and I wanted to determine what the probability of this happening is. (This is unordered sampling without replacement.)

Assuming that:

  • There are 11 orange M&Ms in a bag
  • There are 55 total M&Ms in a bag

Then I calculate that the probability of pulling three oranges from the bag are:

$\dfrac{\text{all the ways to pull three oranges from the bag}}{\text{all the ways to pull three of any color from the bag}} = \dfrac{{11}\choose{3}} {{55}\choose{3}} = 0.0062$

(computed on Wolfram Alpha)

Is this correct, or am I mistaken?

  • 2
    $\begingroup$ The probability is closer to $0.0063$, but the procedure is correct. There are other ways, such as $\frac{11}{55}\cdot\frac{10}{54}\cdot \frac{9}{53}$. $\endgroup$ – André Nicolas Jan 2 '14 at 4:35
  • $\begingroup$ Perhaps you wish to use the word probability instead of odds...? $\endgroup$ – Benjamin Dickman Jan 2 '14 at 7:28

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