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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 qualitycontrol 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.
 Summer '06
 imnotsure
 Calculus, Probability

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