Contemporary Mathematics- MAT 130
Probability
Solve the following problems:
1. A fair die is tossed.
a) What is the probability of obtaining a number less than 4?
b) What is the probability of obtaining a number less than 7?
c) What is the probability of obtaining a number less than 1?
2. Two coins are flipped.
a) What is the probability of obtaining exactly two heads?
b) What is the probability of obtaining exactly one head?
3. A box contains 2 black marbles, 5 blue marbles and 4 red marbles. What is the probability
that a random chosen marble will be:
a) Black?
b) Not red?
c) Not blue?
4. A card is drawn from a standard deck of cards ( 52 cards)
a) What is the probability that the card is an ace?
b) What is the probability that the card is the ace of spades?
c) What is the probability that the card is not a jack?
d) What is the probability that the card will be a spade?
e) What is the probability that the card will not be a spade?
5. A box contains 2 black marbles, 5 blue marbles and 4 red marbles. Two marbles are picked
one after the other with replacement.
a) What is the probability that the first marble will be black and the second marble will be
blue?
b) What is the probability that the first one is black and the second one is not blue?
Bergen Community College Learning Assistance Center
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Phone Number:
201-447-7489
Contemporary Mathematics- MAT 130
Probability
6. A box contains 2 black marbles, 5 blue marbles and 4 red marbles. Two marbles are picked
one after the other without replacement.
a) What is the probability that the first marble will be black and the second marble will be
blue?
b) What is the probability that the first one is black and the second one is not blue?
7. Two dice are rolled.
a) Find the probability that the sum turning up is 6.
b) Find the probability of getting an even number on the first die and an odd number on the
second one.
8. The probability of an event is 5/7.
a) Find the odds in favor of this event occurring.
b) Find the odds against this event occurring.
9. The odds in favor of an event occurring are 5 : 8.
a) What are the odds against this event occurring?
b) What is the probability that the event will not occur?
10. The probability of an Earthquake in a given year is 1/50.
a) What is the probability of getting an earthquake two consecutive years?
b) What is the Probability of getting an earthquake the first year and the third year, but not
the second year?
11. Three light bulbs are connected in parallel. Thus there will be light as long as one of the light
bulbs works. The probability of a light bulb malfunctioning is 1/10.
a) What is the probability of all three of the light bulbs malfunctioning?
b) What is the probability of none of the light bulbs malfunctioning?
Bergen Community College Learning Assistance Center
Room: L-125
Phone Number:
201-447-7489
Contemporary Mathematics- MAT 130
Probability
12. Two cards are drawn in succession (one after the other) from a deck of 52 cards.
a) What is the probability that the first card is a king and the second card is the ace of
spades?
b) What is the probability that the first card is a jack and the second card is an ace?
c) What is the probability that both cards are queens?
d) What is the probability that neither card is a queen?
13. The probability that it is Monday and a student does not show up for class is 0.05.
a) What is the probability that it is Monday?
b) What is the probability that a student does not show up for class given that it is Monday?
14. At BCC 38 % of the students take math, and 26% of the students take math and English.
What is the probability of a student taking English, given that they are taking math?
15. A jar contains blue and red marbles. Two marbles are chosen without replacement. The
probability of selecting a blue marble is 0.37. The probability of selecting a blue marble and
a red marble is 0.26.What is the probability of selecting a red marble given that the first
marble drawn was blue?
16. A teacher gave her class two tests. 27% of the class passed both tests and 53% of the class
passed the first test. What percent of the students who passed the first test also passed the
second test?
17. During the winter season the probability of catching a cold is 0.30, and the probability of
getting a sore throat as a result of catching the cold is 0.17. Find the probability that a
person will catch a cold and have a sore throat.
18. A coin and a die are tossed.
a) What is the probability of getting a tail and a 2?
b) What is the probability of getting a 2 given that you got a head from the coin?
c) What is the probability of getting a tail and an odd number?
d) What is the probability of getting an even number on the die?
Bergen Community College Learning Assistance Center
Room: L-125
Phone Number:
201-447-7489
Contemporary Mathematics- MAT 130
Probability
19. A coin is tossed. If you get a tail you win a point, if you get a head you lose a turn.
a) What is the probability of getting 2 points in a row?
b) What is the probability of getting 3 points in a row?
c) What is the probability of losing a turn, given that you won a point?
20. A coin is tossed. If tails comes up a die is rolled.
a) What is the probability of obtaining two heads?
b) What is the probability of getting a 2?
c) What is the probability of obtaining an even number?
Bergen Community College Learning Assistance Center
Room: L-125
Phone Number:
201-447-7489
Contemporary Mathematics- MAT 130
Probability
Answers:
1.
a)
3 1

6 2
b) 1
c) 0
2.
a)
1
4
b)
1
2
a)
2
11
b)
7
11
c)
6
11
a)
4
1

52 13
b)
1
52
c)
48 12

52 13
3.
4.
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Contemporary Mathematics- MAT 130
d)
13 1

52 4
e)
39 3

52 4
a)
2 5 10
 
11 11 121
b)
2 6 12
 
11 11 121
a)
2 5 10
1
 

11 10 110 11
b)
2 5 10
1
 

11 10 110 11
a)
5
36
b)
1
4
Probability
5.
6.
7.
8.
a) 5 : 2
b) 2 : 5
9.
a) 8 : 5
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Phone Number:
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Contemporary Mathematics- MAT 130
Probability
b)
8
13
a)
1 1
1
 
50 50 2500
b)
1 49 1
49
  
50 50 50 125000
a)
1 1 1
1
  
10 10 10 1000
b)
9 9 9
729
  
10 10 10 1000
a)
4 1
4
1
 

52 51 2652 663
b)
4 4
16
4
 

52 51 2652 663
c)
4 3
12
3
1
=
 

52 51 2652 663 221
d)
48 47 2256 188



52 51 2652 221
a)
1
Since there are seven days in a week
7
10.
11.
12.
13.
b)
0.05
 0.35
1
7
14.
0.26
 0.68
0.38
15.
0.26
 0.703
0.37
Bergen Community College Learning Assistance Center
Room: L-125
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Contemporary Mathematics- MAT 130
16.
0.27
 0.51
0.53
Probability
17. 0.17  0.30  0.051
18.
a)
1 1 1
 
2 6 12
b)
1
(ignore probability of the coin toss)
6
c)
1 3 1 1 1
   
2 6 2 2 4
d)
3 1

6 2
a)
1 1 1
 
2 2 4
b)
1 1 1 1
  
2 2 2 8
c)
1
2
a)
1 1 1
 
2 2 4
b)
1 1 1
 
2 6 12
c)
1 3 1 1 1
   
2 6 2 2 4
19.
20.
Bergen Community College Learning Assistance Center
Room: L-125
Phone Number:
201-447-7489