l09_cond_prob

# l09_cond_prob - Conditional Probability Reading Ross Ch 3...

This preview shows pages 1–8. Sign up to view the full content.

02/23/2009 CS206 - Intro. to Discrete Structures II 1 Conditional Probability Reading: Ross, Ch 3., Sec. 1-2 & 5. Wednesday, February 25, 2009

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

View Full Document
02/23/2009 CS206 - Intro. to Discrete Structures II 2 Example Two dice, 36 equally likely outcomes. E 1 : first dice is 3. E 2 : sum of two dice = 6. P(E 1 )= ? P(E 2 ) = ? P(E 2 if E 1 happened) = ? (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) E 1 E 2 Wednesday, February 25, 2009
02/23/2009 CS206 - Intro. to Discrete Structures II 3 Example (cont’d) Ω = {(1,1),…,(6,6)} E 1 = {(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)} E 2 = {(5,1),(4,2),(3,3),(2,4),(1,5)} E 1 E 2 = {(3,3)} P(E 1 ) = |E 1 |/| Ω | = 6/36 = 1/6 P(E 2 ) = |E 2 |/| Ω | = 5/36 P(E 1 ,E 2 ) = P(E 1 E 2 ) = |E 1 E 2 |/| Ω |=1/36 Wednesday, February 25, 2009

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

View Full Document
02/23/2009 CS206 - Intro. to Discrete Structures II 4 Example (cont’d) P(E 2 if E 1 happened) = ? Ω n = Ω if E 1 happened = E 1 E n = E 2 if E 1 happened = E 2 E 1 = {(3,3)} P(E 2 if E 1 happened) = |E n | / | Ω n | = |E 2 E 1 | / |E 1 | = 1/6 Notation: P(E 2 if E 1 happened) = P(E 2 | E 1 ) – “E 1 given E 2 Given Wednesday, February 25, 2009
02/23/2009 CS206 - Intro. to Discrete Structures II 5 Example (cont’d) P(E 2 | E 1 ) = |E 2 E 1 | / |E 1 | = ( |E 2 E 1 | / | Ω | ) / ( |E 1 | / | Ω | ) = P(E 1 ,E 2 ) / P(E 1 ) Wednesday, February 25, 2009

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

View Full Document
02/23/2009 CS206 - Intro. to Discrete Structures II 6 Conditional Probability Let there be two events, A and B µ Ω . The conditional probability of A|B is P(A|B) = P(A,B) / P(B) when P(B)>0. A (or B) – consequence B (or A) – cause Wednesday, February 25, 2009
02/23/2009 CS206 - Intro. to Discrete Structures II 7 Example I Assume you have a bin with 25 light bulbs. Of those, 5 are good (will last over 2 months), 10 are cheap (will last less that 2 months), and 10 are defective . We install one light bulb, come back a day later and notice the bulb is still lit.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern