Download Probability and Statistics EQT 272

Probability and Statistics EQT 272
Semester 2
2011/2012
TUTORIAL 1
1. In an assessment for students who took Engineering Mathematics I course, it is known
that the percentage of students who passed in their monthly test is 80% while 85%
passed their quiz and 75% passed in both monthly test and quiz. A students is selected
at random, calculate the probability that
a) passed the monthly test or quiz
b) passed the monthly test but failed quiz
c) failed both monthly test and quiz
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:
a) P( A)
b) P( B)
c) P( A)
d) P( A  B)
e) P( A  B)
3) Toss two fair coins and record the outcome. There are the events of interest:
A: observe at least one head
B: observe at least one tail
C: observe exactly one head in the two tosses
(Show your tree diagram)
Define the events A, B, C , A  B  C , A  B  C and A as collections of simple
events and find their probabilities.
4) A couple has three children. Draw a tree diagram for the possible gender of the three
children. Find the probability of getting:
i) Three boys
ii) One boy and two girls
5) 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 colors. What is the
probability that both candies are red?
Probability and Statistics EQT 272
Semester 2
2011/2012
6) A piece of equipment is composed of five parts that can be assembled in any order. A
test is to be conducted to determine the time necessary for each order of assembly. If
each order is to be tested once, how many tests must be conducted?
7) A printed circuit board may be purchased from seven suppliers. In how many ways
can three suppliers be chosen from the seven?
8) 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? What is the probability the child chooses 2 yellow
balls, 1 red ball and 1 blue ball?
9) 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?
10) Among 400 randomly selected drivers in the 20-24 brackets, 136 were involved in an
accident the previous year. If a driver in that age bracket is randomly selected, what is
the probability he/she will be involved in an accident?
11) A company produces 10 microchips during a nightshift. 6 of these turn out to be
defective. Suppose 3 of the chips were sent to a customer. What is the probability of
the customer receiving 2 defective chips? No defective chips?
12) A digital lock has 3 dials, each with 10 positions. How many possible “dial
combinations” are there for this lock? What is the probability a person who does not
know the combination will get it right the first time?
13) A college’s record shows that 7% of its students had been of the Dean’s list. 16%
receives scholarship, 2% had been on the dean’s list and receives scholarship. Find
the probability a student
a) receives scholarship or has been on the dean’s list.
b) has never been on the dean’s list.
Probability and Statistics EQT 272
Semester 2
2011/2012
14) 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.
15) How many four-letter code words are possible using the letters in TYPE if
a)
b)
the letters may be repeated?
the letters may not be repeated?
16) Suppose that in the general population, there are 51% men and 49% women, and that
the proportion of colorblind men and women are shown in the probability table below:
Colorblind (A)
Not Colorblind (A’)
Total
Men (B)
0.04
0.47
0.51
Women (B’)
0.002
0.488
0.49
Total
0.042
0.958
1.00
i) If a person is drawn at random from this population and is found to be a man
(event B), what is the probability that the man is colorblind (event A)?
ii) What is the probability of being colorblind, given that the person is female?
17) The table below is the result of a survey done on customer’s satisfaction for a certain
brand of computer:
Satisfied
Laptop
Desktop
Yes
320
80
No
14
36
a) Find the probability of selecting a satisfied customer given he bought a laptop.
b) Find the probability of selecting a laptop customer given he is not a satisfied
customer.
c) Find the probability of selecting satisfied desktop customer.
Probability and Statistics EQT 272
Semester 2
2011/2012
d) Find the probability of selecting a satisfied laptop customer.
18) 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?
19) If P( A | B)  0.4, P( B)  0.8 and P( A)  0.5, are the events A and B independent?
20) If P( A | B)  0.3, P( B)  0.8 and P( A)  0.3, are the events B and A independent?
21) 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.
a) How many percent of all computers used by the government agencies are
defective?
b) A computer is found to be defective. What is the probability it was supplied by
company B?