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Department of Mathematics
Centre for Foundation Studies, IIUM
Semester III, 2012/2013
SHF1124 (MATH II)
TUTORIAL 4
CHAPTER 4: PROBABILITY AND COUNTING RULES
Page
Number
Section
Questions
6.1 Counting Rules
268 – 269 3, 5, 9, 15, 17
6.2 Sample Spaces & Probability
278 - 279
3, 6, 9
6.3 The Addition Rules for Probability
285 - 286
2, 6, 7
6.4
The
Multiplication Rule
Conditional Probability
6.5 Probability and Counting Rules
295 – 296
6, 7, 10
302 – 304
5, 9, 10
306 - 308
4, 11, 17
Chapter 6 REVIEW EXERCISES
and
*Required Textbook: - Salina Mohin et al , Mathematics & Statistics for Pre-University,
McGraw-Hill Education (Malaysia) Sdn Bhd.(2013)
EXTRA QUESTIONS
1. In how many ways can the letters in the word ‘MOTIVATION’ be arranged if
(i)
The two ‘T’s must be next to each other?
(ii)
The two ‘T’s must be seperated?
2. Eight students are to be separated into two distinct teams, Blue team and Red team. Each
team must contain at least two students. How many ways can this be done if the number
of students in Blue team and Red Team are unequal?
3. In arranging a ten-day examination timetable involving 10 different subjects, a teacher
planned not to have Biology and Statistics on consecutive days. How many ways are
possible?
4. DNA molecules consist of chemically linked sequences of the bases adenine, guanine,
cytosine and thymine denoted A, G, C and T respectively. A sequence of three bases is
called a codon.
(i)
How many different codons are there?
(ii)
The bases A and G are purines, while C and T are pyrimidines. How many codons
are there whose first and third bases are purines and whose second base is a
pyrimidine?
(iii) How many codons consist of three different bases?
5. A History class consists of 15 male and 12 female students. Three of the male students
and five of the female students are non-bumiputras. A student is randomly selected. Find
the probability of selecting:
(i)
a bumiputra student.
(ii)
a female student given that the student is a non-bumiputra.
(iii) either a male or non-bumiputra student
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6. In a process that manufactures aluminum cans, the probability that a can has a flaw on
its side is 0.02, the probability that a can has a flaw on the top is 0.03, and the probability
that a can has a flaw on both the side and the top is 0.01.
(a) Three cans are randomly chosen and inspected. Find the probability that
(i)
the three cans have flaw.
(ii)
at least one can has flaw.
(b) A can is randomly chosen. Find the probability that a can will have a flaw on the side,
given that it has a flaw on top?
7. The proportion of people in a given community who have a certain disease is 0.005. A
test is available to diagnose the disease. If a person has the disease, the probability that
the test will produce a positive signal is 0.95. If a person does not have the disease, the
probability that the test will produce a positive signal is 0.08. A person is chosen at
random.
(i)
What is the probability of the person getting positive signal?
(ii)
If a person tests negative, what is the probability that the person has the disease?
8. An envelope contains the 22 stamps describe below:
Blue
Orange
Used
4
5
Unused
7
6
Three of these stamps, which represent a random selection from the 22 stamps have fallen out of
the envelope and are missing. The events A and B defined as:
A : No blue stamps are missing
B: At least one of the unused stamps is missing
Find:
(i)
(ii)
(iii)
P(A)
P(B)
P(B|A)
9. Four apples are selected at random from a lot of 10 apples. On inspection, it was found that 4 of
the apples are green and they are all good. The other 6 are red and 2 of the red ones are rotten.
Events X and Y are defined as follows:
X: event that of the 4 apples chosen, 2 are green and 2 are red.
Y: Event that of the 4 apples chosen, one is rotten.
Find:
(i)
P(Y)
(ii)
P(X ∩ Y)
(iii)
P(X | Y)
̅ )= 2p. Find:
10. For the events A and B, P(B)= p, P(A|B)=p2,
(i)
P(A) and ̅ ∩ in terms of p.
(ii)
the value of p if the event ̅ and ̅ are mutually exclusive and p < 1.
“… But it is possible that you dislike a thing which is good for you, and that you
love a thing which is bad for you. But Allah knows, and you know not.”
(Al-Baqarah : 216)
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ANSWERS for Extra Questions:
1.
(i) 90720 ways
(ii) 362880 ways
2.
3.
4.
168 ways
2,903,040 ways
(i) 64
(ii) 8
(iii)24
5.
i) 19/27
ii) 5/8
iii) 20/27
6.
(a) i) 6.4 x 10-5
ii) 0.1153
(b)0.33
7.
(i) 0.08435
(ii) 2.73 x 10-4
8.
(i) 0.1071
(ii) 0.9455
(iii)0.9398
9.
(i) 0.5333
(ii) 0.2286
(iii)0.4286
10. (i) P(A)= p3 – 2p2 + 2p
P( ̅ ∩ B = p – p3
(ii)p =
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