Probability (6) Conditional probability

Probability (6) Conditional probability - Conditional...

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

View Full Document Right Arrow Icon
Conditional probability
Image of page 1

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

View Full Document Right 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.
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.
Image of page 3

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

View Full Document Right 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}.
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
Image of page 5

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

View Full Document Right 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.
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
Image of page 7

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

View Full Document Right 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)?
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern