Probability (6) Conditional probability

Probability(6) - Conditional probability Conditional probability So far all(unconditional probabilities were calculated with respect to the sample

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Conditional probability
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
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.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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}.
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 2 On page 21 of the course note Now we randomly select one of these 50 students, then what is the probability
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/09/2010 for the course ENGLISH 1303 taught by Professor May during the Spring '10 term at HKU.

Page1 / 30

Probability(6) - Conditional probability Conditional probability So far all(unconditional probabilities were calculated with respect to the sample

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online