CHAPTER 5 REVIEW QUIZ (11 POINTS)
Use the following to answer questions 1-4:
A system has two components that operate in parallel, as shown in the diagram below. Because
the components operate in parallel, at least one of the components must function properly if the
system is to function properly. The probabilities of failures for the components 1 and 2 during
one period of operation are .20 and .03, respectively. Let F denote the event that component 1
fails during one period of operation and G denote the event that component 2 fails during one
period of operation. The component failures are independent.
1
Input
Output
2
1. The event corresponding to the above system failing during one period of operation is
A) F  G.
B) F  G.
C) Fc  Gc.
D) Fc  Gc.
Ans: A
2. The event corresponding to the above system functioning properly during one period of
operation is
A) F  G.
B) F  G.
C) Fc  Gc.
D) Fc  Gc.
Ans: C
3. The probability that the system functions properly during one period of operation is
closest to
A) 0.994.
B) 0.970.
C) 0.940.
D) 0.776.
Ans: A
4. The probability that the system fails during one period of operation is closest to
A) 0.230.
B) 0.224.
C) 0.060.
D) 0.006.
Ans: D
5. A small class has 10 students. Five of the students are male and five are female. I write
the name of each student on a 3  5 card. The cards are shuffled thoroughly and I
choose one at random, observe the name of the student, and replace it in the set. The
cards are thoroughly reshuffled and I again choose a card at random, observe the name,
and replace it in the set. This is done a total of four times. Let X be the number of cards
observed in these four trials with a name corresponding to a male student. The random
variable X has which of the following probability distributions?
A) The normal distribution, with mean 2 and variance 1.
B) The binomial distribution, with parameters n = 4 and p = 0.5.
C) The Poisson distribution, with  = 4/10.
D) None of the above.
Ans: B
6. A set of 10 cards consists of five red cards and five black cards. The cards are shuffled
thoroughly and I choose six of these at random. Let X be the number of red cards
observed in the six chosen. The random variable X has which of the following
probability distributions?
A) The normal distribution with mean 3 and variance 1.22.
B) The binomial distribution with parameters n = 6 and p = 0.5.
C) The Poisson distribution with  = 6/10.
D) None of the above.
Ans: D
Use the following to answer questions 7-9:
A garment manufacturer knows that the number of flaws per square yard in a particular type of
cloth that he purchases varies with an average of 1.3 flaws per square yard. The count X of flaws
per square yard can be modeled by a Poisson distribution.
7. Using the Poisson probability formula, the probability of getting exactly two flaws in a
randomly selected yard of cloth is
A) 0.2169.
B) 0.3012.
C) 0.3614.
D) 0.6626.
Ans: A
8. Using the Poisson probability formula, the probability of getting at most one flaw in a
randomly selected yard of cloth is
A) 0.2169.
B) 0.3012.
C) 0.3614.
D) 0.6626.
Ans: D
9. The standard deviation of the number of flaws in a randomly selected yard of cloth is
A) 1.14.
B) 1.30.
C) 1.61.
D) 1.69.
Ans: A
Use the following to answer questions 10-11:
An event A will occur with probability 0.5. An event B will occur with probability 0.6. The
probability that both A and B will occur is 0.1.
10. The conditional probability of A given B is
A) 0.3.
B) 0.2.
C) 1/6.
D) not able to be determined from the information given.
Ans: C
11. We may conclude
A) events A and B are independent.
B) events A and B are disjoint.
C) either A or B always occurs.
D) none of the above.
Ans: C