New Quiz 1 Solutions

New Quiz 1 Solutions - P(A B) = ᴗ P(A) + P(B) - P(A B) =...

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STA 3032 Engineering Statistics New Quiz 1 Solutions Spring 2011 Problem 4.10 [Page 166]: A manufacturing company has two retail outlets. It is known that 30% of the potential customers buy products from outlet I alone = P(A B c ) 50% buy from outlet II alone = P(A c B) 10% buy from both I and II and = P(A B) 10% buy from neither = P(A c B c ) = 1 – P[Not(A B)] {DeMorgan’s Law!} Let A denote the event that a potential customer, randomly chosen buys from I And let B denote the event that a randomly chosen potential customer buys from II. i) [Added] Explain in words what each of the following events means. ii) Find the probabilities of each event. [Hint: A correct Venn diagram will be very helpful.] a) A means a randomly selected potential customer buys from outlet I P(A) = P(A B c ) + P(A B) = 0.30 + 0.10 = 0.40 b) A B means a randomly selected potential customer buys from outlet I or outlet II or from both I and II.
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Unformatted text preview: P(A B) = ᴗ P(A) + P(B) - P(A B) = 0.40 + 0.60 - 0.10 = 0.90 ᴖ Since P(B) = P(A c B) + P(A B) = 0.50 + 0.10 = 0.60 ᴖ ᴖ c) B c means a randomly selected customer does not buy from outlet II . P(B c ) = 1 – P(B) = 1 – 0.6 = 0.40 d) A B means ᴖ a randomly selected potential customer buys from both I and II. P(A B) ᴖ = 0.10 e) A B ᴗ c means a randomly selected potential customer buys either from I or does not buy from II P(A B ᴗ c ) = P(A) + P(B c ) – P(A B ᴖ c ) = 0.40 + 0.40 – 0.30 = 0.50 f) Not(A B) means ᴖ a randomly selected potential customer does not buy from both outlet I and outlet II. P[Not(A B)] = ᴖ 1 – P(A B) = 1 – 0.10 = 0.90 ᴖ g) Not(A B) means ᴗ a randomly selected potential customer does not buy from outlet I only or from outlet II only, nor from outlet I and II. P[Not(A B)] = ᴗ 1 – P(A B) = 1 – 0.90 = 0.10 ᴗ...
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This note was uploaded on 04/04/2012 for the course STA 3032 taught by Professor Kyung during the Fall '08 term at University of Florida.

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