概率论快速学习03：概率公理补充

Written In The Font

　　I like maths when i was young,but I need to record them. So I am writing with some demos of Python

Content

　　If two events, A and B are independent then the joint probability is

For example, if two coins are flipped the chance of both being heads is

In Python

A = set([1,2,3,4,5])
B = set([2,4,3,5,6])
C = set([4,6,7,4,2,1])

print(A & B & C)

Output:

{2, 4}

# & find the objects the same in Set

　　 If either event A or event B or both events occur on a single performance of an experiment this is called the union of the events A and B denoted as:

　　If two events are mutually exclusive then the probability of either occurring is

For example, the chance of rolling a 1 or 2 on a six-sided die is

In Python

A = set([1,2,3,4,5])
B = set([2,4,3,5,6])
C = set([4,6,7,4,2,1])

print(A | B | C)

Output:

{1, 2, 3, 4, 5, 6, 7}

# | find all the objects the set has

　　If the events are not mutually exclusive then

Proved

For example:

　　Let’s use Python to show u an example about devil's bones (骰子,不是魔鬼的骨头哈)

A = set([1,2,3,4,5,6])  # the all results of devil's bones
B = set([2,4,3])        # the A event results
C = set([4,6])          # the B event results 

P_B =  1/2
P_C =  1/3

D = B | C
print(D)

P_D = 2/3

print(P_D == (P_B+P_C - 1/6))

Output:

{2, 3, 4, 6}
True

Let me show u some others :

If u r tired , please have a tea , or look far to make u feel better.If u r ok, Go on!

　　Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written:

　　Some authors, such as De Finetti, prefer to introduce conditional probability as an axiom of probability:

^①

Given two events A and B from the sigma-field of a probability space
with P(B) > 0, the conditional probability of A given Bis defined as
the quotient of the probability of the joint of events A and B, and the
probability of B:　　

　　^②

　　the ①② expressions are the same. Maybe u can remember
one , the other will be easy to be coverted.So I am going to tell an
excemple to let u remmeber it(them):

　　“the phone has a power supply (B), the phone can be used to call others(A).”

　　One → : When the phone has a full power supply , u can call others.

　　Two →P(B): has a power supply

　　Three = One + Two → U can call others about your love with others.

do u remember it?