MA375: Solution to a homework problem from this week or last week's homework

Spring 2009, Prof. Walther


6.1 #38

Coin tossed 3 times. Possible Outcomes: TTT HHH TTH HHT THT HTH THH HTT

Are the following independent? ie. p(A intersection B) = p(A)* p(B)

a. First coin tails Second coin heads First coin tails and Second coin heads

        4/8                      4/8                           2/8

(1/2)*(1/2) = 1/4 INDEPENDENT


b. First coin tails Two, and not three heads come up in a row Intersection: First coin tails, and then the last 2 are heads

         4/8                           2/8                                                   1/8

(1/2)*(1/4) = 1/8 INDEPENDENT


c. Second coin tails Two, and not three heads come up in a row

          4/8                               2/8                  

Intersection: Second coin must be tails, and then the last 2 slots must be 2 heads in a row

                           0

(1/2)*(1/4) = 0 False, DEPENDENT


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