Reading notes: Sheldon Ross: Fundamentals of probability theory tutorial: Random variables

Example 1b a jar with a ball numbered 1-20, no back to extract 3, take out the ball at least one number greater than or equal to 17 probability is what?

In addition to the solution in the book, there is a solution:

Consider the opposite: the number of three balls is less than 17.

The first time from the number 1-16 to take one, 16 kinds of extraction, the remaining 15 balls;

The second time from the number 1-16 to take one, 15 kinds of extraction, the remaining 14 balls;

The third time from the number 1-16 to take a, 14 kinds of extraction.

Such a common 16x15x14 seed extraction. But wait! This type of extraction is considered in order, but in fact the number of balls taken three times is 1, 2, 3 and 3, 2, 1, respectively.

So the extraction is 16x15x14/3! species.

So the final probability is 1-16x15x14/3!/c (3,20) =0.5088

Reading notes: Sheldon Ross: Fundamentals of probability theory tutorial: Random variables