What are the chances to draw exactly one card of four in a sixty card deck? This is exactly the question the hypergeometric distribution answers. Here are two graphs showing this distribution. First, the height of the bars shows the percentage of hands that have exactly the specified number of cards. The red bars show chances for drawing exactly one card of four. As you can see the maximum value is about 44% when 15 cards are drawn. This also happens to be when the average or mean value is exactly one.

Here is the same data with the bars stacked to show that the percentages always add to 100. This view clearly shows that your chance to draw at least one of the four cards after drawing fifteen is about 69%.

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