Maths Quest Maths A Year 12 for Queensland
WorkSHEET 9.2
Chapter 9 Probability and the binomial distribution WorkSHEET 9.2
1
Probability and the binomial distribution
Name: ___________________________
1
/50
6
In a class of 25 students, 11 study History and
12 study Geography. There are 5 students who
study both History and Geography. Draw a
Venn diagram showing the distribution of the
students in these subjects.
11 study History and 5 study History and
Geography
 6 study History only.
12 study Geography and 5 study History and
Geography
 7 study Geography only.
There are 25 students in total. So, the number
who study neither of these subjects
= 25 – (6 + 5 + 7)
=7
2
In a group of 100 students, it was found that 40 (a)
study Maths A, 30 study Drama and 54 study
neither.
(a) Draw a Venn diagram to display this
information.
(b)
If a student is chosen at random, what is
the probability that this student studies
Drama but not Maths A?
6
40  30  54  124
There are only 100 students
So, overlap  124  100
 24
 Number studying Maths A only
 40  24
 16
Number studying Drama only
 30  24
6
(b)
PD but not M   PD only 
6

100
 0.06
Maths Quest Maths A Year 12 for Queensland
3
Chapter 9 Probability and the binomial distribution WorkSHEET 9.2
A survey of a class of 30 students found that 12
owned a dog, 10 owned a cat and 16 owned
neither. How many students had both a cat and
a dog?
2
4
Total number of students  30
10  12  16  38
 Overlap  8
So, 8 students own both.
4
A survey of the reading habits of 500 people
found that:
130 read magazines
180 read non-fiction
220 read novels
40 read magazines and novels
20 read magazines and non-fiction
30 read novels and non-fiction
5 read all three
How many read none of these?
5
4
500  (135 + 15 + 5 + 25 + 75 + 35 + 155)
= 55 read none of these.
In a class it was found that 64% of the students
like apples, 48% like bananas and 21% like
(a)
both.
(a) Draw a Venn diagram showing the
student preference.
(b)
Find the probability that a student chosen
at random is one who likes neither apples
nor bananas.
6
Percentage liking apples only  64  21
 43%
Percentage liking bananas only  48  21
 27%
 Percentage liking neither
 100  43  21  27 
 9%
(b)
P(likes neither apples nor bananas) = 0.09
Maths Quest Maths A Year 12 for Queensland
6
Chapter 9 Probability and the binomial distribution WorkSHEET 9.2
A survey of students in a class revealed that, in
the year to date, 56% of the students had been
on a holiday within Australia, 37% had been
on an overseas holiday and 26% had been on
both.
PO   0.37
P(both A and O)  0.26
P(either A or O)
 P(A)  P(O)  P (both A and O)
 0.56  0.37  0.26
 0.67
Write Pascal’s triangle to row 5.
1
1
1
1
Use Pascal’s triangle to determine the
probability of tossing 3 tails in 4 tosses of a
coin.
6
1
1
8
3
PA   0.56
Use the Addition Rule for Probability to
determine the probability that a student chosen
at random had either been on an Australian or
overseas holiday.
7
3
2
3
4
5
1
6
10
1
3
1
4
10
1
5 1
p  Psuccess 
 PT 
 0.5
q  Pfailure
 PH 

 0.5
n  4 trials
P3 tails in 4 tosses   4 p 3 q1
 4  0.5  0.5
 0.25
5
Maths Quest Maths A Year 12 for Queensland
9
Chapter 9 Probability and the binomial distribution WorkSHEET 9.2
If the coin in question 8 was biased so that it
landed tail up 70% of the time, what would be
the probability of getting at least one tail in the
four tosses.
p  Psuccess 
4
5
 PT 
 0.7
q  Pfailure
 PH 

 0.3
n  4 trials
Pat least 1 T   1  Pno T 
 1  P4H 
 1 q4
 1  0.34
 0.9919
10
Use the Binomial Cumulative Distribution
Tables in your textbook to answer the
following question.
In a multiple-choice test of 20 questions there
are 5 options: A, B, C, D or E. Through purely
guessing, what is the probability of passing the
test?
Use the Binomial Cumulative Distribution
Tables on pages 455–56.
n  20
p  Psuccess 
 Pcorrect answer 
1
5
 0 .2

P 10 correct   1  P 9 correct 
 1  0.9974
 0.0026
So the probability of passing by purely
guessing = 0.0026.
5