01_21ans - STAT 400 Examples for Spring 2011 1 Suppose a...

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

View Full Document Right Arrow Icon
STAT 400 Examples for 01/21/2011 Spring 2011 1. Suppose a 6-sided die is rolled. The sample space, S , is { 1, 2, 3, 4, 5, 6 } . Consider the following events: A = { the outcome is even } , B = { the outcome is greater than 3 } , a) List outcomes in A, B, A ' , A B, A B. A = { the outcome is even } = { 2, 4, 6 } , B = { the outcome is greater than 3 } = { 4, 5, 6 } , A ' = { 1, 3, 5 } , A B = { 4, 6 } , A B = { 2, 4, 5, 6 } . b) Find the probabilities P( A ), P( B ), P( A ' ), P( A B ), P( A B ) if the die is balanced (fair). P( A ) = 3 / 6 , P( B ) = 3 / 6 , P( A ' ) = 3 / 6 , P( A B ) = 2 / 6 , P( A B ) = 4 / 6 .
Image of page 1

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

View Full Document Right Arrow Icon
c) Suppose the die is loaded so that the probability of an outcome is proportional to the outcome, i.e. P( 1 ) = p , P( 2 ) = 2 p , P( 3 ) = 3 p , P( 4 ) = 4 p , P( 5 ) = 5 p , P( 6 ) = 6 p . i) Find the value of p that would make this a valid probability model. P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1.0. p + 2 p + 3 p + 4 p + 5 p + 6 p = 21 p = 1.0. p = 1 / 21 . ii) Find the probabilities P( A ), P( B ), P( A ' ), P( A B ), P( A B ). P( A ) = P(2) + P(4) + P(6) = 2 / 21 + 4 / 21 + 6 / 21 = 12 / 21 . P( B ) = P(4) + P(5) + P(6) = 4 / 21 + 5 / 21 + 6 / 21 = 15 / 21 . P( A ' ) = 1 – P( A ) = 1 – 12 / 21 = 9 / 21 . OR P( A ' ) = P(1) + P(3) + P(5) = 1 / 21 + 3 / 21 + 5 / 21 = 9 / 21 .
Image of page 2
Image of page 3
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