Choose two keys from 10, and * * has c (10/0,2) = 45 methods.

Two of the keys can't open the door, so there is a method of C (7 7,2) = 21.

So the probability of not opening the door is 2 1/45 = 7/ 15.

The probability of opening the door is1-7/15 = 8/15.

For example:

1/ 15= 1/5* 1/3

The probability that B wins C is 1/5, and the probability that B wins A is 1/3.

The probability that A wins B is p1=1-1/3 = 2/3.

The probability of defeating C P2 =( 1/6)/(2/3)= 1/4.

P(x=0)= 1/3 *3/4= 1/4

p(x = 3)= 1/3 * 1/4+2/3 * 3/4 = 7/ 12

P(x=6)=2/3* 1/4= 1/6

ex = 3 * 7/ 12+6 * 1/6 = 1 1/4

Extended data:

Introduce "probability" into the quantification of event possibility. Is there a stable value for the total number of independent repetitions n, event A frequency μ, event A frequency Fn(A)=μ/n, and event A frequency Fn(A)? If yes, the stable value p of the frequency μ/n is called the probability of the occurrence of event A, and it is recorded as P(A)=p (statistical definition of probability).

P(A) is objective, while Fn(A) depends on experience. In statistics, the value of Fn(A) is sometimes used as an approximation of probability when n is large.

Baidu encyclopedia-probability