Probabilities of drawing red and blue balls without replacement


What is the probability of drawing red and blue balls from a jar of red and blue balls?
Check which to select:
Only red balls, Enter number:

Only blue balls, Enter number:

red: then blue balls:


The number of red and blue balls in the jar is shown at right, from which you pick balls at random. If you picked in sequence the red and blue balls without replacing them as specified above, then the probability for this to have happened is shown on the right (and above). The equation to calculate the probabilities is quite simple and relies on multiplying the ratios of the individual probabilities of selecting a ball. For example, if one has 3 red and 5 blue balls (a total of 8 balls) in the jar, then if the first blind pick is a red ball then this has a probability of 3/8. If the second blind pick is another red ball then this has a probability of 2/7 (since there are only 2 red balls when the selection was made, and only 7 total balls because a red ball was taken away). The probability of the two red balls being drawn is then 3/8 * 2/7 = 6/56 = 0.0107142857.
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