Question 1

At Billʹs community college, 41.7% of students are Caucasian and 2.7% of students are Caucasian math majors.What percentage of Caucasian students are math majors?
A) 6.5%
B) 15.4%
C) 39.0%
D) 44.4%

Accepted Answer

To find the percentage of Caucasian students who are math majors, divide the percentage of Caucasian math majors (2.7%) by the percentage of Caucasian students (41.7%) and multiply by 100: (2.7 / 41.7) * 100 = 6.5%.

Question 2

390 voters are classified by income and political party. The results are shown in the table. If a person isselected at random from the sample, find the probability that the person has high income. $$\begin{array} { l c c c } 
\hline & \text { Democrat } & \text { Republican } & \text { Total } \
\hline \text { Low Income } & 108 & 69 & 177 \
\text { Medium Income } & 91 & 74 & 165 \
\text { High Income } & 18 & 17 & 35 \
\text { Super High Income } & 8 & 5 & 13 \
\text { Total } & 225 & 165 & 390 \
\hline
\end{array}$$
A) 0.090
B) 0.046
C) 0.080
D) 0.514

Accepted Answer

The probability that a person has high income is calculated by dividing the total number of people with high income by the total number of people surveyed. From the table, there are 35 people with high income out of 390 people surveyed, so the probability is $ \frac{35}{390} = 0.090$.

Question 3

The table below describes the exercise habits of a group of people suffering from high blood pressure. If one ofthe 1046 subjects is randomly selected, find the probability that the person selected is female given that theyexercise occasionally. $\begin{array}{r|cccr} 
& \begin{array}{c}
\text { No } \
\text { exercise }
\end{array} & \begin{array}{c}
\text { Occasional } \
\text { exercise }
\end{array} & \begin{array}{c}
\text { Regular } \
\text { exercise }
\end{array} & \text { Total } \
\hline \text { Men } & 384 & 85 & 74 & 543 \
\text { Women } & 345 & 69 & 89 & 503 \
\text { Total } & 729 & 154 & 163 & 1046
\end{array}$

A) 0.448
B) 0.066
C) 0.137
D) 0.147

Accepted Answer

The probability that the person selected is female given that they exercise occasionally is calculated using the formula for conditional probability: P(A|B) = P(A and B) / P(B), where A is the event of being female and B is the event of exercising occasionally. Here, P(A and B) is the number of women who exercise occasionally (69), and P(B) is the total number of people who exercise occasionally (154). Thus, the probability is 69/154 = 0.448.

Question 4

A poet will read 4 of her poems at an award ceremony. How many ways can she choose the 4 poems from 9poems given that the sequence is important?
A) 3024
B) 15,120
C) 126
D) 30,240

Accepted Answer

The number of ways to choose 4 poems out of 9 with sequence being important is calculated using permutations: 9P4 = 9! / (9-4)! = 9*8*7*6 = 3024.

Question 5

390 voters are classified by income and political party. The results are shown in the table. If a person isselected at random from the sample, find the probability that the person has medium income and votesDemocrat. $$\begin{array} { l c c c } 
\hline & \text { Democrat } & \text { Republican } & \text { Total } \
\hline \text { Low Income } & 102 & 77 & 179 \
\text { Medium Income } & 94 & 66 & 160 \
\text { High Income } & 23 & 14 & 37 \
\text { Super High Income } & 6 & 8 & 14 \
\text { Total } & 225 & 165 & 390 \
\hline
\end{array}$$
A) 0.241
B) 0.418
C) 0.588
D) 0.746

Accepted Answer

The probability that a randomly selected person has medium income and votes Democrat is calculated by dividing the number of medium income Democrats (94) by the total number of people (390), which gives $ \frac{94}{390} \approx 0.241 $.

Question 6

In how many ways can a board of supervisors choose a president, a treasurer, and a secretary from its 6members ?
A) 120
B) 216
C) 720
D) 20

Accepted Answer

The board can choose a president in 6 ways, a treasurer in 5 ways (after choosing the president), and a secretary in 4 ways (after choosing the president and treasurer), leading to 6*5*4 = 120 ways.

Question 7

A company makes skirts in 5 different styles. Each style comes in two different fabrics and 3 different colors.How many skirts are available from this company?
A) 30
B) 15
C) 8
D) 10

Accepted Answer

For each of the 5 styles, there are 2 fabric options and 3 color options. So, for each style, there are 2 * 3 = 6 variations. Since there are 5 styles, the total number of skirts available is 5 * 6 = 30.

Question 8

At a certain college, 13% of students speak Spanish, 7% speak Italian, and 3% speak both languages. A studentis chosen at random from the college. What is the probability that the student speaks Spanish given that he orshe speaks Italian?
A) 0.429
B) 0.231
C) 0.040
D) 0.170

Accepted Answer

To find the probability that a student speaks Spanish given they speak Italian, we use the formula for conditional probability: P(A|B) = P(A and B) / P(B). Here, A is the event of speaking Spanish, and B is the event of speaking Italian. Given that P(A and B) = 0.03 (3% speak both) and P(B) = 0.07 (7% speak Italian), P(A|B) = 0.03 / 0.07 = 0.429.

Question 9

Karen is completing a fitness circuit. There are 11 fitness stations. At each station she can choose from 4different activities. If she chooses one activity at each fitness station, in how many ways can she complete thecircuit?
A) 4,194,304
B) 44
C) 14,641
D) 15

Accepted Answer

Since Karen has 4 choices at each of the 11 stations, the total number of ways she can complete the circuit is $4^{11} = 4,194,304$.

Question 10

A pool of possible candidates for a student council consists of 10 freshmen and 8 sophomores. How manydifferent councils consisting of 5 freshmen and 7 sophomores are possible?
A) 2016
B) 18,564
C) 206,841,600
D) 3,628,800

Accepted Answer

The answer of A pool of possible candidates for a...

Question 11

How many arrangement are there of the letters DISAPPOINT?
A) 907,200
B) 3,628,800
C) 1,814,400
D) 1024

Accepted Answer

The word DISAPPOINT has 10 letters in total, with the letter P repeated twice. The total number of arrangements can be calculated using the formula for permutations of a multiset: $n! / (n_1! \cdot n_2! \cdot \ldots \cdot n_k!)$, where $n$ is the total number of items to arrange, and $n_1, n_2, \ldots, n_k$ are the counts of each repeated item. Here, $n = 10$ and $n_1 = 2$ (for the two Ps), so the total number of arrangements is $10! / 2! = 3,628,800 / 2 = 1,814,400 / 2 = 907,200$.

Question 12

How many different arrangements are possible using 6 letters from the word PAYMENT?
A) 5040
B) 2520
C) 7
D) 42

Accepted Answer

The word PAYMENT has 7 distinct letters. The number of different arrangements of 6 letters from these 7 is calculated using the permutation formula, which is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to choose. Here, n=7 and r=6, so P(7, 6) = 7! / (7-6)! = 7! / 1! = 7! = 5040.

Question 13

If a coin is tossed 9 times, how many head-tail sequences are possible?
A) 512
B) 18
C) 362,880
D) 81

Accepted Answer

Each coin toss has 2 possible outcomes (head or tail), and since there are 9 tosses, the total number of possible sequences is 2^9 = 512.

Question 14

License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition ofletters and digits is allowed?
A) 67,600
B) 10,000
C) 456,976
D) 6760

Accepted Answer

There are 26 possibilities for each letter and 10 possibilities for each digit. Since repetition is allowed, the total number of plates is $26^2 \times 10^2 = 676 \times 100 = 67,600$.

Question 15

There are 12 runners in a race. In how many ways can the first, second, and third place finishes occur? (Assumethere are no ties.)
A) 1320
B) 220
C) 1324
D) 218

Accepted Answer

This is a permutation problem because the order in which the runners finish matters. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items (runners) and r is the number of items being chosen (top 3 finishers). Here, n=12 and r=3, so the calculation is 12P3 = 12! / (12-3)! = 12! / 9! = 12 x 11 x 10 = 1320.

Question 16

66% of students at one college drink alcohol regularly, and 13% of those who drink alcohol regularly sufferfrom depression. What is the probability that a randomly selected student drinks alcohol regularly and suffersfrom depression?
A) 0.0858
B) 0.79
C) 0.7042
D) 0.5742

Accepted Answer

To find the probability that a student both drinks alcohol regularly and suffers from depression, multiply the probability of a student drinking alcohol regularly (66% or 0.66) by the probability that a student who drinks suffers from depression (13% or 0.13): 0.66 * 0.13 = 0.0858.

Question 17

In how many ways can Iris choose 4 of 13 books to bring on vacation?
A) 715
B) 17,160
C) 24
D) 28,561

Accepted Answer

The number of ways Iris can choose 4 out of 13 books is calculated using the combination formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of items (13 books), k is the number of items to choose (4 books), and "!" denotes factorial. Thus, C(13, 4) = 13! / [4!(13-4)!] = 13! / (4!9!) = (13×12×11×10) / (4×3×2×1) = 715.

Question 18

The table below describes the exercise habits of a group of people suffering from high blood pressure. If awoman is selected at random from the group, find the probability that she does not exercise. $$\begin{array} { r | c c c r } 
& \begin{array} { c } 
\text { No } \
\text { exercise }
\end{array} & \begin{array} { c } 
\text { Occasional } \
\text { exercise }
\end{array} & \begin{array} { r } 
\text { Regular } \
\text { exercise }
\end{array} & \text { Total } \
\hline \text { Men } & 358 & 66 & 87 & 511 \
\text { Women } & 352 & 86 & 76 & 514 \
\text { Total } & 710 & 152 & 163 & 1025
\end{array}$$
A) 0.685
B) 0.343
C) 0.496
D) 0.501

Accepted Answer

The answer of The table below describes the exercise habits...

Question 19

390 voters are classified by income and political party. The results are shown in the table. If a person isselected at random from the sample, find the probability that the person has medium income or votesDemocrat. $$\begin{array} { l c c c } 
\hline & \text { Democrat } & \text { Republican } & \text { Total } \
\hline \text { Low Income } & 107 & 75 & 182 \
\text { Medium Income } & 92 & 67 & 159 \
\text { High Income } & 19 & 19 & 38 \
\text { Super High Income } & 7 & 4 & 11 \
\text { Total } & 225 & 165 & 390 \
\hline
\end{array}$$
A) 0.749
B) 0.409
C) 0.579
D) 0.985

Accepted Answer

To find the probability that a person has medium income or votes Democrat, we add the number of people with medium income (159) to the number of Democrats (225), and then subtract the overlap (Democrats with medium income, which is 92) to avoid double counting. This gives us $159 + 225 - 92 = 292$. The probability is then $292 / 390 = 0.749$.

Question 20

Suppose that the probability that Sue will pass her statistics test is 0.62, the probability that she will pass herphysics test is 0.48, and the probability that she will pass both tests is 0.290. What is the probability that shepasses her physics test given that she passed her statistics test?
A) 0.468
B) 0.604
C) 0.190
D) 0.810

Accepted Answer

P(Physics|Statistics) = P(Physics and Statistics) / P(Statistics)= 0.290 / 0.62= 0.468

Quiz 5: Probability

At Billʹs community college, 41.7% of students are Caucasian and 2.7% of students are Caucasian math majors.What percentage of Caucasian students are math majors?

A poet will read 4 of her poems at an award ceremony. How many ways can she choose the 4 poems from 9poems given that the sequence is important?

In how many ways can a board of supervisors choose a president, a treasurer, and a secretary from its 6members ?

A company makes skirts in 5 different styles. Each style comes in two different fabrics and 3 different colors.How many skirts are available from this company?

At a certain college, 13% of students speak Spanish, 7% speak Italian, and 3% speak both languages. A studentis chosen at random from the college. What is the probability that the student speaks Spanish given that he orshe speaks Italian?

Karen is completing a fitness circuit. There are 11 fitness stations. At each station she can choose from 4different activities. If she chooses one activity at each fitness station, in how many ways can she complete thecircuit?

A pool of possible candidates for a student council consists of 10 freshmen and 8 sophomores. How manydifferent councils consisting of 5 freshmen and 7 sophomores are possible?

How many arrangement are there of the letters DISAPPOINT?

How many different arrangements are possible using 6 letters from the word PAYMENT?

If a coin is tossed 9 times, how many head-tail sequences are possible?

License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition ofletters and digits is allowed?

There are 12 runners in a race. In how many ways can the first, second, and third place finishes occur? (Assumethere are no ties.)

66% of students at one college drink alcohol regularly, and 13% of those who drink alcohol regularly sufferfrom depression. What is the probability that a randomly selected student drinks alcohol regularly and suffersfrom depression?

In how many ways can Iris choose 4 of 13 books to bring on vacation?

Suppose that the probability that Sue will pass her statistics test is 0.62, the probability that she will pass herphysics test is 0.48, and the probability that she will pass both tests is 0.290. What is the probability that shepasses her physics test given that she passed her statistics test?