Sciences Mathematics College Math College Math Exams Probability, Sets, And Venn Diagrams
Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items. How many backpacks contained none of the three writing instruments?
A) 3
B) 11
C) 2
D) 15
Explanation:
In a survey of 24 college students, it was found that 16 were taking an English class, 17 were taking a math class, and 10 were taking both English and math. How many students were taking a math class only?
A) 8
B) 7
C) 18
D) 1
Explanation:
Find the general term of the set. {–9, –4, 1, 6, 11, . . .}
A) 5n-14
B) -14n+ 5
C) 3n-12
D) n-10
Explanation:
Find the number of subsets the set has. {1, 2, 3, 4}
A) 15
B) 4
C) 8
D) 16
Explanation:
If a set has n elements, then there are 2n subsets. Hence, 24 = 16
Two dice are rolled. Find the probability of getting a 5 on either die or the sum of both dice is 5.
A) 11/36
B) 1/6
C) 7/18
D) 1/3
Explanation:
In a shop there are 20 customers, 18 of whom will make a purchase. If three customers are selected, one at a time, at random, what is the probability that all will make a purchase?
A) 0.7158
B) 0.7605
C) 0.8524
D) 0.8808
Explanation:
A single card is drawn from a deck. Find the probability of selecting a 3 or a club.
A) 7/52
B) 17/52
C) 4/13
D) 9/26
Explanation:
The odds in favor of an event are 10:1. Find the probability that the event will occur.
A) 9/11
B) 10/11
C) 1/10
D) 9/10
Explanation:
How many 3-digit codes using the digits 0 through 9 are possible if repetitions are allowed?
A) 504
B) 30
C) 1000
D) 729
Explanation:
The first digit can choose 10 different ways. Since repetitions are allowed, the second digit can choose 10 different ways. Also, the third digit can choose 10 different ways. So, the possible 3-digit codes using the digits 0 through 9 with repetitions allowed is: 10 x 10 x 10 = 1000.
A lottery has one $5000 prize, two $3000 prizes, and ten $1000 prizes. Five thousand tickets are sold at $5 each. Find the expectation if a person buys three tickets.
A) –$0.80
B) –$1.60
C) –$2.40
D) –$3.20
Explanation:
Let U = {5, 10, 15, 20, 25, 30, 35, 40}
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find BC
A) {30, 40}
B) {25, 35}
C)
D) {5, 15}
Explanation:
Find all proper subsets of the set. {c, f, y}
A) ; {c, f}; {c, y}; {f, y}; {c, f, y}
B) ; {c}; {f}; {y}; {c, f}; {c, y}; {f, y}; {c, f, y}
C) ; {c}; {f}; {y}; {c, f}; {c, y}; {f, y}
D) ; {c, f}; {c, y}; {f, y}
Explanation:
A proper subset is a subset which is not the same as the original subset itself. For example, {a, b} is a proper subset of {a, b, c}, but {a, b, c} is not a proper subset of {a, b, c}.
A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is not blue?
A) 1/11
B) 5/16
C) 11/16
D) 1/5
Explanation:
If two people are selected at random, what is the probability that they were both born in May?
A) 1/6
B) 1/132
C) 1/12
D) 1/144
Explanation:
Four red cards are numbered 1, 2, 3, and 4. Three black cards are numbered 5, 6, and 7. The cards are placed in a box and one card is selected at random. What is the probability that a red card was selected given that the number on the card was an even number?
A) 2/3
B) 1/3
C) 1/2
D) 3/4
Explanation:
