Math Methods
Name_______________________
Chapter 14-15
Statistics & Probability Supplemental
Problems 
1. Two letters are selected at random from the word ATTITUDE.
(a) If the letters are selected with the first one selected being
replaced before the second one is made:
1. are the events independent?
2. What is the probability that both letters are Ts?
3. what is the probability that both letters are vowels?
(b) If the letters are selected without replacement:
1. are the events independent?
2. what is the probability that both letters are Ts?
3. what is the probability that both letters are vowels?
2. In a group of 80 students, 35 play baseball, 25 play football and 30
play neither.
i. Draw a Venn diagram to show these data
ii. What is the probability that a randomly selected student plays
both baseball and football?
iii. What is the probability that a randomly selected student plays
baseball but not football?
iv. What is the probability that a randomly selected student plays
neither sport?
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3. Two events A and B are such that p A  0.4 , p B  0.3
find the probability of the following events:
b g
. ,
and p A  B  01
i. A  B '
ii. A B
iii. B A'
iv. A' B'
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b g 43 .
4. A and B are events with P A  x, P B  2 x and P A  B 
b g
Using the
expansion for P A  B , find x in each of the following cases:
a. A and B are mutually exclusive
b. A  B
c. A and B are independent
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a. Pb
A  Bg b.
c h
Pc
B Ah
5. If P A  0.4, P B  0.7 and P A B  0.3 , find
c.
c
h
P A A B
6. In a Football competition, 12 teams play a series of matches to
determine the best 5 (which then play a further series of “finals”).
Before the start of this season, “The Moon” newspaper ran a contest
in which readers were invited to select the 5 teams that they
expected to be the successful ones. The order was not important, and
there were no restrictions on the number of entries per person.
a. Wendy wanted to submit a sufficient number of entries to ensure
that one of them must be correct. How many must she submit?
b. In fact, nobody selected the correct 5 teams, so the prize was
divided among those who selected 4 correct. How many different
selections could have qualified for this prize?
7. As a result of a certain random experiment, the events A and/or B may
occur. These events are independent, and P A  0.5; P B  0.2
a. Find the probability that both A and B occur
b. Find the probability that neither A nor B occurs
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8. A box contains three coins, one of which is known to be ‘doubleheaded’.
a. If a coin is selected at random and tossed, find the probability
that it falls ‘heads’
b. If a coin selected at random falls ‘heads’ when tossed, what is
the probability that it is the double-headed coin.
9. The letters of the word GENERAL are arranged at random in a row.
Find the probability that:
a. G precedes L
b. G immediately precedes L
c. Both E’s occur together
10.
A mathematics competition consists of fifteen multiple-choice
questions each having four choices with only one choice correct.
Allan works through this test and he knows the correct answer to the
first seven questions, but he does not know anything at all about the
remaining questions, so he guesses. Find the probability that he
gets exactly 12 correct.
11.
In a certain country 65% of the population support Ben’s Party
and 35% support Sam’s Party. 90% of Ben’s Party and 40% of those who
support Sam’s Party believe that Ben is a good leader. A member of
the population is chosen at random. Given that the person believes
Ben is a good leader find the probability that the person supports
Ben’s Party.
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12.
Three Italian, two Chemistry and four Physics books are to be
arranged on a shelf. In how many ways can this be done
a. If there are no restrictions?
b. If the Chemistry books must remain together?
c. If the books must stay together by subject?
13.
5 boys and 5 girls, which include a brother-sister, pair are to
be arranged in a straight line. Find the number of possible
arrangements if
a. there are no restrictions
b. the tallest must be at one end and the shortest at the other end
c. the brother and sister must be
i. together
ii.
Separated
14.
A tennis club has 20 members
a. In how many ways can a committee of 3 be selected?
b. In how many ways can this be done if the captain must be on the
committee?
15.
In how many ways can a jury of 12 be selected from 9 men and 6
women so that there are at least 6 men and no more than 4 women on
the jury?
16.
In how many ways can 4 women and 3 men be arranged in a circle?
In how many ways can this be done if the tallest woman and the
shortest man must be next to each other?
17.
A family has three children.
find the probability that
List the sample space and hence
a. There are 3 boys
b. There are 2 boys and 1 girl
c. There are at least two girls
18.
A pack of cards contains 4 red and 5 black cards. A hand of 5
cards is drawn without replacement. What is the probability of all
five black? Of exactly three black?
19.
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c h
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b g
1
1
5
Let A and B be events such that P A  , P B  and P A  B 
3
4
12
a. Find P A B
b. P A B'
c. are A and B independent?
Why?
c h
ANSWERS:
1a1. yes 1a2. 649
1a3. 41
1b1. no 1b2. 283
1b3. 143
2ii. 81 2iii.
5
2iv. 83 3i. 0.8 3ii. 13 3iii. 13 3iv. 0.4 4a. 41
4b. 83 4c.
16
.219 5a. 0.89 5b. .525 5c. .45 6a. 792 6b. 35 7a. 0.1 7b.
0.4
189
8a. 23 8b. 21
9a. ½
9b. 17
9c. 72
10. 8192
11. 0.807 12a. 362880
12b. 80640 12c. 1728 13a. 3628800 13b. 80640 13ci. 725760 13cii.
2903040 14a. 1140 14b. 171 15. 155 16. 720; 240
1
17. 8 in sample space 17a. 81 17b. 83 17c. 21
18. 126
19a. 23
19b.
; 10
21
2
19c. nope
9
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