pset_05_spring2012_solutions

# pset_05_spring2012_solutions - Statistics 100 Spring 2012...

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Statistics 100 — Spring 2012 — Problem Set 5 Solutions 1. IPS 4.28 (a) How can we verify a legitimate assignment of probabilities? By showing that they sum to 1 (and note they are all between zero and one): 0 . 000+0 . 036+0 . 003+0 . 121+ . 060+0 . 691+0 . 062+0 . 027 = 1 (b) Pr( A ) = Pr( Hispanic ) = 0 . 000 + 0 . 003 + . 060 + 0 . 062 = 0 . 125 (c) What is the complement of B in words? B C is the event that a randomly chosen American is not white. What is its probability, using the complement rule? Pr( B c ) = 1 - Pr( B ) = 1 - (0 . 060 + 0 . 691) = 1 - 0 . 751 = 0 . 249 (d) The expression ”The person chosen is a non-Hispanic white” can be expressed symbolically as ( A C and B ) . Its probability is Pr( A c and B ) = 0 . 691 . Note, we cannot multiply Pr( A c ) Pr( B ) since the 2 events are not independent. 2. PINs For each digit we have a choice of any number from 0-9 so the total number of PINs possible is 10 4 . To see this you can imagine a tree with ten branches to represent the ten choices for the first digit. Attached to each of these branches is ten more branches to represent the choices for the second digit.

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