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Consider picking a white marble out a "success". The probability of having 100 successes in 100 trials is p^100, where p is the success probability.
For the case where there actually are 100 white marbles in the jar, p is equal to 1. Calculating the sum of p^100 for p = 0, 0.01, 0.02...0.99, 1.00, you get approximately 1.572.
1 / 1.572 = 0.636; there is a 63.6% chance that, given the condition that you picked 100 white marbles, the jar contains only white marbles.
Another way to think of that second part is this: Imagine you have 10,000 of these jars. 100 of them have no white marbles, 100 of them have just 1 white marble, 100 of them have 2 white marbles...etc, and 100 of them have 100 white marbles.
If you conducted this trial on all 10,000 jars, you would expect to get all white marbles about 157 times. Of those 157 times, 100 of them resulted from the jars that only contained white marbles. Therefore, 100 / 157 = 63.6%. |
