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Lecture 9

MATH 141 Lecture 9: Statistics 10/11/2016
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Department
MATH - Mathematics
Course Code
MATH 141
Professor
Zhang

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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 proaility of otaiig a  = /6
What is the proaility agai of otaiig a  if you ko the uer is ee already?
1/3
Conditional probability
Based on an event B in the past (Reason Event: you know my number is even) to
foreast the eet A otaiig 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 ad A? Whats the relatioship?
Rolling a fair dice twice,
1. Koig the st result is , hat is the proaility 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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Description
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 probability of obtaining a ‘2’ = 1/6  What is the probability again of obtaining a ‘2’ if you know the number is even already? 1/3 Conditional probability  Based on an event B in the past (Reason Event: you know my number is even) to forecast the event A (obtaining a ‘2’) in 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|
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