# note06 - Section 2.3 Conditional Probability and...

This preview shows pages 1–3. Sign up to view the full content.

Section 2.3: Conditional Probability and Independence The conditional probability of event A given B , where p ( B ) negationslash = 0, is the proba- bility that event A occurs given that event B has occurred. P ( A | B ) = P ( A B ) P ( B ) The multiplicative rule is simply the conditional probability rule rewritten. P ( A B ) = P ( A | B ) · P ( B ) or P ( A B ) = P ( B | A ) · P ( A ) Two events A and B are independent if P ( A | B ) = P ( A ) or P ( B | A ) = P ( B ) , as long as P ( A ) and P ( B ) does not equal to 0. A and B are said to be independent if the occurrence of one does not affect the probability of the occurrence of other. Exercise 1. Show that p ( A B ) = P ( A ) · P ( B ) if A and B are independent.

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

View Full Document
2. The probability that a microchip fails on its first use is 0 . 10. Given that a microchip lasts through its first use, the probability that it lasts a year is 0 . 99. What is the probability that the chip does not fail during its first year (including first use)?
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