Exercises Week 2.docx - Probability Data Tutorial 1 1 Class has 50 students;20 male(M 25 brown-eyed(B For a randomly chosen student what is the range of

Exercises Week 2.docx - Probability Data Tutorial 1 1 Class...

This preview shows page 1 - 3 out of 6 pages.

Probability & Data Tutorial 1 1. Class has 50 students;20 male (M), 25 brown-eyed (B). For a randomly chosen student what is the range of possible values for P ( M B ) ? 2. Let A, B and C be sets, Use Venn diagrams to show the following: (a) The 2nd distributive law A ∩ ( B C ) = ( A∩ B ) ( A∩ C ) , (b) The 2nd De-Morgan's Law ´ A ∩B = ´ A ´ B. Use the lecture notes and Venn Diagrams to prove the above. 3. Explain from the basis of C r n , why P r n = r !×C r n . 4. A committee consisting of 1 President, 2 Vice-Presidents and 1 Treasurer is selected from a society consisting of 10 members. (a) How many ways can we select the committee? (b) How many ways can we arrange the committee in a row at the front of the stage, if the 2 Vice-President positions are considered equal? (c) How many ways can we arrange the committee around a round table, if the 2 Vice-President positions are considered equal? 5. Use Venn diagrams and the Probability Axioms to show that P ( A B C ) = P ( A ) + P ( B ) + P ( C ) P ( A∩ B ) P ( B∩C ) P ( A∩C ) + P ( A∩ B∩C ) .
Image of page 1
6. Show that if A B , then P ( A ) ≤ P ( B ) . 7. What is the probability of getting 3 tails in 5 tosses of a fair coin? Please use a counting method for this question - in a later chapter we will discuss the binomial distribution, where this sort of probability can be calculated by using a formula.
Image of page 2
Image of page 3

You've reached the end of your free preview.

Want to read all 6 pages?

  • Three '19
  • Cho-Chnge Kow

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

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes