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Statistics

10/11/2016

Conditional probability and its application – Case difference

Independent/Dependent events

Let say we have events A and B.

If the result of event A does NOT influence the result of event B, we say these events are

independent. Otherwise, they are dependent.

If event A and B are independent,

because we need to get event A done first step and B for the second step.

Rolling a fair dice

What is the proaility of otaiig a = /6

What is the proaility agai of otaiig a if you ko the uer is ee already?

1/3

Conditional probability

Based on an event B in the past (Reason Event: you know my number is even) to

foreast the eet A otaiig a i the future.

A|B: The conditional event A, given the reason event B has already happened.

P(A|B): The probability that A happens given the result of B.

A|B ad A? Whats the relatioship?

Rolling a fair dice twice,

1. Koig the st result is , hat is the proaility that e get i the d trial?

2. Without prior information, what is the probability that we consider the second outcome

is ?

What happens if Independence

Independence: Two events A and B, if the results do not influence each other.

Dependence: Consider different results of B, the probability of A will be changed.

A and B are independent P(A|B) = P(A) P(A and B) = P(A) P(B)

Otherwise, A and B are dependent.

Application of Conditional Probability

1. Consider all possible cases to get event A happened.

2. Based on the result of A, see what is the most possible reason for that

Whole probability

Suppose your event A can be triggered due to different reasons B1, B2…BK

Then the chance of you get A happening, consider all possible conditions, is

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