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# 0028 c at least 1 rotten orange solution the at least

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Unformatted text preview: 1) n(S ) = C (75, 5) P (E ) = C (6,3)C (69,2)+C (6,4)C (69,1) C (75,5) ≈ .0028 (C) at least 1 rotten orange? Solution: The “at least 1” means we are going to use the complement rule. If E is the event that at least 1 is rotten, then E c is the event that none is rotten. This means for E c we want 0 of the 6 rotten oranges and 5 of the 69 good oranges. n(E ) = C (6, 0)C (69, 5) n(S ) = C (75, 5) P (E ) = C (6,0)C (69,5) C (75,5) ≈ .6512 (D) all rotten oranges? Solution: We want 5 of the 6 rotten oranges and 0 of the 69 good oranges. n(E ) = C (6, 5)C (69, 0) n(S ) = C (75, 5) P (E ) = .0000003476 Problem 5 What is the probability that at least two of the ﬁve members of a city council share a birthday? Solution: We always use the complement rule for the birthday problem. If E is the event that at least two members share a birthday, then E c is the event that none of the members share a birthday. n(E c ) = 365 × 364 × 363 × 362 × 361 n(S ) = 365 × 365 × 365 × 365 × 365 = 3655 365×364×363×362×361 ***Remember, 3655 365×364×363×362×361 1− ≈ .0271 3655 P (E c ) = P (E ) = this is the probability of the complement. This is not your ﬁnal answer! 4 Problem 6 An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelectronic ﬁrms: A, B, and C. The quality-control department of the company has determined that 5% of the microprocessors produced by ﬁrm A are defective, 5% of those produced by ﬁrm B are defective, and 3.5% of those produced by ﬁrm C are defective. Firms A, B, and C supply 35%, 20%, and 45%, respectively, of the microprocessors used by the company. (A) Draw a tree diagram using the given information. Solution: What is the probability that (B) a randomly selected microprocessor comes from ﬁrm A? Solution: P (A) = .35 (C) a randomly selected microprocessor in not defective? Solution: P (nondef ) = .35(.95) + .2(.95) + .45(.965) ≈ .9568 (D) a randomly selected microprocessor is from ﬁrm C and is defective? Solution: P (C ∩ def ) = .45...
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## This document was uploaded on 03/17/2014 for the course MATH 1331 at Texas Tech.

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