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Probability (6) Conditional probability

# Probability (6) Conditional probability - Conditional...

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Conditional probability

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Conditional probability So far, all (unconditional) probabilities were calculated with respect to the sample space S. However, in many situations, we can obtain some new information such that we can update the sample space. In such cases, we are able to update the probability calculations or to calculate conditional probabilities . More specifically, we can restrict to a smaller sample space, instead of S.
Example 1 Question 1: Flip a fair coin three times. List all the possible outcomes, i.e. find the sample space of this experiment. S = { HHH , HHT , HTH , THH, TTH, THT, HTT , TTT }. Denote by A the event that “heads” occurs at the first time. Find A. A = { H HH, H HT, H TH, H TT}. On page 3 of the course note . 2 1 8 4 ) ( ) ( ) ( = = = S n A n A P New information: exactly two heads are obtained.

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Example 1 = " S A Question 1: Flip a fair coin three times. List all the possible outcomes, i.e. find the sample space of this experiment. S = { HHH , HHT , HTH , THH, TTH, THT, HTT , TTT }. On page 3 of the course note New information: exactly two heads are obtained. S” = { HH T, H T H , T HH }. Given the new information, find the updated P(A) or P(A|S”) { HH T, H T H } . 3 2 ) " ( ) " ( ) " | ( = = S n S A n S A P A = {HHH, HHT, HTH, HTT}.
Example 2 On page 21 of the course note There are 50 students, who can be classified in the following table. Female (F) Male (M) Total Major in Engineering (E) 16 4 20 Not major in Engineering (E C ) 10 20 30 Total 26 24 50

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Example 2 On page 21 of the course note Now we randomly select one of these 50 students, then what is the probability that the student is major in Engineering (E)? All possible selections are equally likely.
Example 2 On page 21 of the course note There are 50 students, who can be classified in the following table. Female (F) Male (M) Total Major in Engineering (E) 16 4 20 Not major in Engineering (E C ) 10 20 30 Total 26 24 50

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Example 2 On page 21 of the course note Now we randomly select one of these 50 students, then what is the probability that the student is major in Engineering (E)?
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