4.5 - (4.5 Definition of conditional probability General...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Conditional probability (4.5) Definition of conditional probability General multiplication rule Probability trees Bayes rule Independence
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 probabilities reflect how the probability of an event can change if we know that some other event has occurred/is occurring. Our brains effortlessly calculate conditional probabilities, updating our “degree of belief” with each new piece of evidence .
Image of page 2
A box contains 10 black balls and 15 white balls. Two balls are drawn randomly from the box The probability that the first ball drawn is black equals 10/25 = 0.4. What is the probability that the second ball drawn is black? Sampling with replacement The answer is obviously 10/25 = 0.4. Sampling without replacement Answer = ?
Image of page 3

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

View Full Document Right Arrow Icon
If the first ball drawn was black, then the probability that the second ball is black would be 9/24, but if the first ball drawn was white, then the probability that the second ball is black would be 10/24. The conditional probability that the second ball is black given that the first ball was black is equal to 9/24. The conditional probability that the second ball is black given that the first ball was white is equal to 10/24. For sampling with replacement, both conditional probabilities are equal to 0.4, which is also the unconditional probability.
Image of page 4
Image of page 5
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