Download TUTORIAL 1 1) A random car is chosen among all

Probability and Statistics EQT 272
Semester 1
2016/2017
TUTORIAL 1
1) A random car is chosen among all those passing through The Store on a certain day.
The probability that the car is red is 0.4, the probability that the driver is a student is
0.3 and the probability that the car is red and the driver is a student is 0.05. A car is
selected at random, calculate the probability that
(i) the car is red or belongs to a student
ans: 0.65
(ii) the car is not red and does not belongs to a student
ans: 0.35
2) The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1,
0.2, 0.4 and 0.2, respectively. Let A denote the event {a, b, c} and let B denote the
event {c, d, e}. Determine the following:
(i) P( A)
ans: 0.4
(ii) P(B)
ans: 0.8
(iii)P( A)
ans: 0.6
(iv) P( A  B)
ans: 1
(v) P( A  B)
ans: 0.2
3) Suppose we randomly select two persons from the members of a club and observe
whether the person selected each time is a man or a woman. Write all the outcomes for
this experiment. Draw the tree diagrams.
4) A candy dish contains one yellow and two red candies. You close your eyes, choose
two candies one at a time from the dish, and record their colours. What is the
probability that both candies are red?
ans: 1/3
5) A printed circuit board may be purchased from seven suppliers. In how many ways
can three suppliers be chosen from the seven?
ans: 35 ways
6) There are 5 yellow balls, 4 red balls and 3 blue balls in a box. In how many ways can
a child choose 4 balls from the box without any particular order? What is the
probability that the child choose 2 yellow balls, 1 red ball and 1 blue ball?
ans: 495 ways, 0.2424
Probability and Statistics EQT 272
Semester 1
2016/2017
7) Suppose 20 students share the same floor of a dormitory. 11 of them took Statistics
class, 8 took Chemistry class and 3 took both Statistics and Chemistry classes. A
student is chosen at random from 20 students. What is the probability he took either
the Statistics or Chemistry classes? What is the probability he did not take any of the
two classes?
ans: 0.8, 0.2
8) Consider the following events for an experiment of rolling a fair dice.
A= an even number is observed
B= an odd number is observed
C= a number less than 4 is observed
Are events A and B mutually exclusive? Are events B and C mutually
exclusive? Draw a venn diagram for events A, B and C.
ans: A and B are mutually exclusive, B and C are not mutually
exclusive
9) How many four-letter code words are possible using the letters in TYPE if
(i) the letters may be repeated?
ans: 256
(ii) the letters may not be repeated?
ans: 24
10) Toss two coins and observe the outcome. Define these events and its probability:
A: head on the first coin
B: tail on the second coin
Are events A and B independent?
ans: A and B are
independent
11) 30% of all computer used by government agencies are supplied by company A and
the rest by company B. 5% of all computers supplied by company A are defective
while 2% of all computers supplied by company B are defective.
(i) How many percent of all computers used are defective?
ans: 2.9%
(ii) A computer is found to be defective. What is the probability it was supplied
by company B?
ans: 0.4828
12) A statistics class for engineers consists of 25 industrial, 10 mechanical,
10electricaland 8 civil engineering students. If a person is randomly selected by
theinstructor to answer a question, find the probability that the student chosen is
(i) an industrial engineering major.
ans: 25/23
(ii) a civil engineering or an electrical engineering major.
ans: 18/53
Probability and Statistics EQT 272
Semester 1
2016/2017
13) John is going to graduate from an industrial engineering department in a university by
the end of the semester. After being interviewed at two companies he likes, he
assesses that his probability of getting an offer from company A is 0.8, and the
probability that he gets an offer from company B is 0.6. If on the other hand, he
believes that the probability that he will get offers from both companies is 0.5, what is
the probability that he will get at least one offer from these two companies?
ans: 0.9
14) Suppose the manufacturer specifications of the length of a certain type of computer
cable are 2000 ± 10 millimeters. In this industry, it is known that small cable is just as
likely to be defective (not meeting specifications) as large cable. That is, the
probability of randomly producing a cable with length exceeding 2010 millimeters is
equal to the probability of producing a cable with length smaller than 1990
millimeters. The probability that the production procedure meets specifications is
known to be 0.99.
(i) What is the probability that a cable selected randomly is too large?
ans: 0.005
(ii) What is the probability that a randomly selected cable is larger than 1990
millimeters?
ans: 0.995