This kind of experiment is called equal probability (or classical probability)
Example 1: There are five balls in a bag, three of which are white balls and two are blue balls, so the possibility of getting each ball is equal.
(1) Take a ball at random from the bag, write A={ white ball}, and find p (a).
(2) Take out two balls from the bag and don't put them back. Remember that B={ both balls are white} and ask.
P(B)。
First, explain the sampling method:
Sampling without putting it back: take out a ball at 1 time, record its color, and take out a ball from the remaining balls at the second time;
Put back sampling: take out a ball at 1 time, record its color, put it back, and take out a ball from all the balls at the second time.
Solution: number the balls. The white balls are 1, 2, 3, and the blue balls are 4, 5.
( 1)
(2)
The number of sample points included is 5x4.
The number of sample points included is 3x2.
Generally speaking, if there are 10 balls, including 10 white balls and 10 blue balls, then take n balls () by no return sampling, and then
Example 2: There are 23 people in the football field (both sides 1 1 player plus 1 referee). What is the probability that at least two of them have the same birthday?
Solution: Suppose everyone's birthday is 365 days a year. So 23 people's birthdays * * * have a possible result.
Consider event A: "Any two people have different birthdays",
It is possible for a to happen.
Therefore,
Example 3: There is a white ball and b blue balls in a bag, a+b = n, assuming that the probability of each ball touching is equal, touch one ball from the bag at a time and touch it n times without putting it back. Find the probability of hitting the white ball for the k th time.
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Solution 1. Number n balls in turn as: 1, 2, ..., n, where the first A is a white ball.
If 1, 2, ..., n is arranged as a sample point, then the probability of each sample point is equal.
Solution 2. Taking the ball number touched for the k th time as the sample point, from the symmetry point of view, the probability of getting each ball is equal.