SRI MANDAPATI S ID: 00746446
EGRM 6609 App Stats – Quality & Engr Mgt
Homework Assignment # 1
1. Explain the concepts of an experiment, outcome, sample space, and event. Provide some
examples different from those in the chapter.
Ans. Experiment–the observation of some activity or the act of taking a measurement
– No of high school students opting for the higher education
–Evaluation of Seismograph reading on daily scale
–Commercials frequency in YouTube
–New courses launches frequency of an educational institute.
Outcome–a particular result of an experiment
–New voter going for the popular leader
– Overall health conditions of a West haven, CT
–Resident in favor of upgrading the technology in areas of residence
–Change in the automation of consumer services on an Average
Sample space -all possible outcomes of an experiment
–No. of recorded tremors in Seismograph during last 5 years
–Weather outcomes: clear, partly cloudy, cloudy
–People willing to work during the crises instead of waiting for the aid
–Change in NASDAQ: positive or negative real number
Event- An event is a collection of one or more outcomes from
–Anticipation of Earth quakes due to the chemical changes in oldest water on earth
–Having a clear or partly cloudy day
–The proportion of respondents that are willing to work in crises
–Having a positive weekly change in the Market closings.
2. Three coins are dropped on a table.
a. List all possible outcomes in the sample space.
b. Find the probability associated with each outcome.
c. Let A be the event “exactly 2 heads.” Find P(A).
d. Let B be the event “at most 1 head.” Find P(B).
e. Let C be the event “at least 2 heads.” Find P(C).
f. Are the events A and B mutually exclusive? Find P(A or B).
g. Are the events A and C mutually exclusive? Find P (A or C).
SRI MANDAPATI S ID: 00746446
Ans.
a) Three coins are dropped on a table and all possible outcomes in the sample space will be
{HHH, HHT, HTH, HTT, TTT, TTH, THT, THH}
b) Probability associated with each outcome of the sample space
P(HHH)= P(HHT)=P(HTH)=P(HTT)=P(TTT)=P(TTH)=P(THT)=P(THH)= 1/8= 0.125
c) A event= “exactly 2heads” P(A) = 3/8 = 0.375
d) B event = “at most 1 head”= P(B)= 7/8 = 0.375
e) C event= “ at least 2 heads”= P(C)= 4/8= 0.5
f) A and B events are not mutually exclusive the P (A or B) = 3/8+7/8-3/8= 7/8= 0.875
g) A and C events are not mutually exclusive the P (A or C) = 3/8+4/8-3/8= 4/8= 0.5
3. A home pregnancy test is not always accurate. Suppose the probability that the test indicates
that a woman is pregnant when she actually is not is 0.02, and the probability the test indicates
that a woman is not pregnant when she really is, is 0.03. Assume that the probability that a
woman who takes the test is actually pregnant is 0.7. What is the probability that a woman is
