1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Independent events in probabilities

  1. Mar 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Let S be the sample space for rolling a single die. Let A={1,2,3,4}, B={2,3,4}, and C={3,4,5}. Which of the pairs (A,B), (A,C), and (B,C) is independent?

    2. Relevant equations

    3. The attempt at a solution
    P(A)=2/3 P(B)=1/2 P(C)=1/2
    P(A&B)=P(A)*P(B)=(2/3)(1/2)=1/3 P(A&B)/P(B)=(1/3)/(1/2)=1/6
    P(A&C)=1/3 P(A&C)/P(C)=(1/3)/(1/2)=1/6
    P(B&C)=1/4 P(B&C)/P(C)=(1/4)/(1/2)=1/8

    So based on my calculations, there is none of the pairs which match the independence rule. But the book says that (A,C) is independent.
  2. jcsd
  3. Mar 15, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    The first and third equations only hold when A and B are independent. The second equation holds generally.
    You can't ignore the outcomes included in each set. For example, if events A and B are both true, that means that you rolled a 2, 3, or 4, so P(A&B)=1/2.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook