ATHS – Math Department Al Ain
Remedial worksheet on Chapter 0 (Lesson 0.4 to 0.6)
ANSWER KEY
Students Name
Class:
Lesson 0.4 (counting Technique)
1) Pizza house offers three different crusts, four sizes and eight
toppings. How many different ways can a customer order a
pizza?
3x4x8=96 ways
2) Omar Math’s quiz has eight true-false questions, how many
different choices for giving answers to the eight questions are
possible?
2x2x2x2x2x2x2x2=256 choices
3) How many different 5 – digit codes are possible if the first digit
cannot be 0 and no digit may be used more than once?
9x9x8x7x6=27216 digit codes
4) A student council committee must be composed of two juniors
and two sophomores, how many different committees can be
chosen from seven juniors and five sophomores?
7C2 x 5C2=
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5) There are 10 finalists in a figure skating competition
How many ways can gold, silver and bronze medals are
awarded?
10 P 3=
6) A newspaper has nine reporters available to cover four different
stories how many ways can the reporters be assigned to cover
the stories?
P= 9 P 4
7) Five cards are drawn from a standard deck of cards. How many
hands consist of three clubs and two diamonds?
13C3 x 13C2=
8) A group of seven students working on a project needs to choose
two students to represent the group’s report. How many ways
can they choose the two students?
P = 7C2
9) Determine whether the situation involves permutation or
combination then find the possibilities. The number of ways can
11 players is selected from 25 to form a football team if each of
the eleven players can play any position
Combination
25C11
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Lesson 0.5 (Adding probability)
1) Suppose that 1400 students , 550 take Spanish , 700 take
biology and 400 take both ,What is the probability that a
student selected at random takes Spanish or biology
P (Spanish or biology) = p(Spanish)+ p(biology) – p (Spanish
and biology)
P (S or B) = P (S) + P (B) – P (S and B)
550 700 400 850
P (S or B) = 1400  1400  1400  1400
2) What is the probability of drawing a king or spade from a deck
of 52 cards
P (King or spade) = P (K) + P (Spade) – P (king and spade)
4 13 1 16 4
P (King or spade) = 52  52  52  52  13
3) There are 7 girls and 6 boys on the junior class committee. A
sub -committee of 4 people is being chosen at random what is
the probability that the sub-committee will have at least 2 girls
P (at least 2 girls) = P (2 girls) + P (3 girls) + P (4 girls)

112
 0.78
143
4) Omar has a stack of 8 baseball cards , 5 basketball cards and
6 soccer cards if he selects a card at random from the stack
what is the probability that it is baseball or soccer card
P(baseball or soccer card ) = P(baseball)+P(soccer)
= 8/19 + 6/19= 14/19
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5) Two cards are drawn from a standard deck of playing cards
Find each probability
a) P ( both queens or both red ) Not Mutually Exclusive
P (both queen) + P (both red) – P (both queen and red)
55
 0.25
221
b) P ( both either black or an ace ) Not Mutually Exclusive
P (both black) + P (both an ace) – P (both black and ace)

55
 0.25
221
6) Determine whether the events are mutually exclusive or not
mutually exclusive then find the probability
a) Two dice are rolled
Find P (sum < 3 or sum > 10)
P (sum < 3 or sum > 10) = 1/36 + 3/36 =4/36= 1/9
b) A card is drawn from a standard playing cards
Find P (jack or red card)
P (jack or red card) = 4/52 + 26/52 – 2/52=28/52=7/13
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7) There are 40 vehicles on a rental car lot. All are either sedans or
SUV’s.
Red
Blue
Black
total
Sedans
3
6
5
14
SUV’S
15
9
2
26
total
18
15
7
40
a) There are 18 red vehicles, and 3 of them are sedans.
b) There are 15 blue vehicles, and 9 of them are SUVs.
c) Of the remaining vehicles all are black and 2 are SUVs.
A vehicle is selected at random
Find the probability
a) P ( blue or black )
P ( blue or black ) = p(blue)+p(black)
= 15/40 + 4/40 = 19/40
b) P ( red or SUV )
P ( red or SUV ) = p(red)+p(SUV)-( red and SUV)
= 18/40 + 26/40 – 15/40= 29/40
c) P ( black or sedan )
P ( black or sedan ) = p(black) + p(sedan) - p(black andsedan)
= 7/40 + 14/40 -5/40=16/40
8) Reasoning: Explain why the rule P(A or B) = P(A) + P(b) – P(A
and B) can be used for both mutually exclusive and not mutually
exclusive events.
When the events are mutually exclusive, P(A and B) will always
be equal to zero, so the probability will simplify to P(A) + P(B).
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Lesson 0.6(Multiplying probability)
1) A jar, contains 4 red marbles 3 green and 2 blue. If a marble is
drawn at random what is the probability that it is not green?
P
6 2

9 3
2) A coin is tossed and a die is rolled what is the probability of a
head and 3?
P
1 1
1
 
2 6 12
3) What is the probability of getting heads each time if a coin is
tossed 3 times?
P
1 1 1 1
  
2 2 2 8
4) In a board game three dice are rolled what is the probability that
the first die shows a 6, the second die shows a 6 and the third
die does not?
P
1 1 5
5
  
6 6 6 216
5) Three cards are drawn from a standard deck of cards without
replacement Find the probability of drawing a diamond, a club
and another diamond in that order?
P
13 13 12
13



52 51 50 850
6) A bag contains 12 red, 9 blue, 11 yellow and 8 green marbles, if
two marbles are drawn at random and not replaced what is the
probability that a red and then a blue marble are drawn?
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P
12 9
9


40 39 130
7) At a restaurant 25% of customers orders chili. If 4 % of
customers order chili and a baked potato , find the probability that
someone who orders chili also orders a baked potato
P ( ordering chili and baked potato) = P( ordering chili) . p(ordering
baked potato)
0.04 = 0.25 x P( ordering baked potato)
P( ordering baked potato) = ( 0.04 / 0.25 )= 0.16
8) The table shows attendance of a wedding. Find the probability
that the person can attend the wedding given that the person is in
the bride’s family
Bride’s family
Can attend
Can’t attend
104
32
136
Groom’s
Family
112
14
126
216
46
P = 104 /136 = 0.76
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9) The table shows the number of students who play baseball
Find the probability that a student plays baseball given that
the student is senior.
10) Suppose the probability that a student takes AP calculus and
is set on the honor roll is 0.0035 , and the probability that a
student is on the honor roll is 0.23 Find the probability that a
student takes AP calculus given that he is on the honor roll .
0.0035 = 0.23 x P( taking AP calculus)
P( taking AP calculus) = ( 0.0035/0.23)= 0.015
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Questions from past EOT exams
1. How many ways are there to choose first, second and third, if there were 5
finalists?
A. 5
B. 30
C. 60
D. 120
E. 1
2. A die is rolled twice. What is the probability of getting 2 fives?
A. 1/36
B. 1/16
C. 1/6
D. 16
E. 36
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