E=n*E 1

Note: e is the mathematical expectation, E 1 is the mathematical expectation of drawing the ball once, and n is the number of times of drawing.

Example: There are identical black balls, white balls and red balls *** 15, including 7 black balls, 3 white balls and 5 black balls.

Then the mathematical expectation of drawing five black balls is E=5*(5/ 15)=5/3.

Derivative problems include pumping people, pumping products and so on

Second, the mathematical expectation of the red light problem

E=P 1+P2+…… ..

Note: p is probability, and e is the sum of all corresponding p.

Example: Xiaohong has four red lights on her way to school, and the probability of encountering 1 red light is 0.5, the second is 0.35, the third is 0.65, and the fourth is 0.23 (the red lights are independent and do not affect each other).

Then Xiaohong's mathematical expectation of running a red light on her way to school is e = 0.5+0.35+0.65+0.23 =1.73.

There are many derivative problems.

Third, the expectation of two wins in three games.

E=2( 1+P 1*P2)

Note: e is the expected number of matches, P 1, and P2 is the winning probability of two teams or two people (P 1+P2= 1).

For example, when A and B play chess, the probability of A winning is 0.45, and that of B winning is 0.55.

Then their expectation of winning two out of three games is E=2( 1+0.45*0.55)=2.495.

The derivative problem is very common in competitions.