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Unformatted text preview: Math 418 Assignment 1–due Wed. Sept. 23 Final Version. N denotes the set of natural numbers. 1. A poker hand has two pair if it contains two cards of one rank, two cards of a second distinct rank and a last card of a third and distinct rank. Find P (two pair and the hand has all cards of the same colour) . 2. Let Ω = N and F = { A ⊂ N : A or A c is finite } . (a) Show that F is a field but not a σfield of subsets of Ω. (b) For A ∈ F , define P ( A ) = braceleftBig if A is finite 1 if A c is finite. Prove that P : F → [0 , 1] is finitely additive but not countably additive on F . Here we say P is countably additive on a field F iff whenever { A n } is a sequence of disjoint sets in F whose union is in F then P ( ∪ A n ) = summationdisplay n P ( A n ) . 3. A factory has two machines A and B that make 60% and 40% of the total production, respectively. Of their output, machine A produces 3% defective items, while machine B produces 5% defective items. Find the probability that a give defective part was producedproduces 5% defective items....
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 Spring '08
 AMJAD

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