Question 1

The Statistics Club at Woodvale College sold college T-shirts as a fundraiser. The results sale are shown below. Choose one student at random. Find the probability that the studen 11-15 T-shirts or less than 6 T-shirts.
$\begin{array}{cc}
\hline \text { No. of t-shirts } & \text { No. of club members } \
\hline 0 & 2 \
1-5 & 13 \
6-10 & 10 \
11-15 & 6 \
16-20 & 5 \
20+ & 2 \
\hline
\end{array}$ f the
A) 0.1579
B) 0.5833
C) 0.5526
D) 0.3947

Accepted Answer

The probability is calculated by adding the number of students who sold 11-15 T-shirts (6) and those who sold less than 6 T-shirts (2 + 13), then dividing by the total number of students (38). So, (6 + 15) / 38 = 21 / 38 = 0.5526.

Question 2

Out of 733 items checked out of a public library, 269 were fiction books, 222 were non-fiction books, and 242 were videos (of any genre). What is the probability that a
Randomly-selected item was not a video?
A) 0.367
B) 0.493
C) 0.67
D) 0.33

Accepted Answer

The probability that a randomly-selected item was not a video is calculated by subtracting the number of videos from the total number of items, and then dividing by the total number of items. So, (733 - 242) / 733 = 491 / 733 ≈ 0.67.

Question 3

If a single card is drawn from an ordinary deck of cards, what is the probability of drawing a jack, queen, king, or ace? 
A) $\frac { 9 } { 26 }$
B) $\frac { 17 } { 52 }$
C) $\frac { 5 } { 13 }$
D) $\frac { 4 } { 13 }$

Accepted Answer

In a standard deck of 52 cards, there are 4 jacks, 4 queens, 4 kings, and 4 aces, totaling 16 cards. Therefore, the probability of drawing a jack, queen, king, or ace is $ \frac{16}{52} = \frac{4}{13} $.

Question 4

An apartment building has the following distribution of apartments:
$\begin{array} { l l l l } & \underline { 1 } \text { bedroom } & \underline { \text { 2 bedroom } } & \underline { \mathbf { 3 } \text { bedroom } } \ \text { 1st floor } & 3 & 1 & 1 \ \text { 2nd floor } & 1 & 3 & 2 \ \text { 3rd floor } & 1 & 4 & 1 \end{array}$
If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms?
A) $\frac { 6 } { 11 }$
B) $\frac { 14 } { 17 }$
C) $\frac { 11 } { 17 }$
D) $\frac { 8 } { 11 }$

Accepted Answer

To find the probability that an apartment is on the 2nd floor or has 2 bedrooms, we first count the total number of apartments, which is 3+1+1+1+3+2+1+4+1 = 17. The number of apartments on the 2nd floor is 1+3+2 = 6. The number of apartments with 2 bedrooms is 1+3+4 = 8. However, the 3 apartments with 2 bedrooms on the 2nd floor were counted twice, so we subtract them once to avoid double counting, giving us 6+8-3 = 11. Therefore, the probability is 11/17.

Question 5

Let $E$ be the event that a corn crop has an infestation of ear worms, and let $B$ be the event that a corn crop has an infestation of corn borers.

Suppose that $P ( E ) = 0.24 , P ( B ) = 0.16$, and $P ( E$ and $B ) = 0.13$. Find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.
A) 0.27
B) 0.53
C) 0.6
D) 0.13

Accepted Answer

The answer of Let $E$ be the event that a...

Question 6

In a fish tank, there are 15 goldfish, 6 angelfish, and 18 guppies. If a fish is selected at random, find the probability that it is an angelfish or a guppy. 
A) $\frac { 11 } { 13 }$
B) $\frac { 8 } { 13 }$
C) $\frac { 7 } { 13 }$
D) $\frac { 5 } { 13 }$

Accepted Answer

The total number of fish is 15 + 6 + 18 = 39. The number of angelfish and guppies combined is 6 + 18 = 24. Therefore, the probability of selecting an angelfish or a guppy is $\frac{24}{39}$, which simplifies to $\frac{8}{13}$.

Question 7

A single card is drawn from a deck. Find the probability of selecting a heart or a 8. 
A) $\frac { 1 } { 4 }$
B) $\frac { 2 } { 13 }$
C) $\frac { 4 } { 13 }$
D) $\frac { 17 } { 52 }$

Accepted Answer

There are 13 hearts and 4 eights in a deck of 52 cards. So, the probability of selecting a heart or a 8 is 13/52 + 4/52 = 17/52 = 4/13.

Question 8

Two dice are rolled. Find the probability of getting doubles or a sum of 2. 
A) $\frac { 1 } { 6 }$
B) $\frac { 2 } { 9 }$
C) $\frac { 7 } { 36 }$
D) $\frac { 1 } { 4 }$

Accepted Answer

The answer of Two dice are rolled. Find the probability...

Question 9

On a certain day, a cheese packaging facility packaged 500 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both majo minor flaws. The following table presents the results.
$\begin{array}{ccc}
\hline & \text { Minor Flaw } & \text { No Minor Flaw } \
\hline \text { Major Flaw } & 16 & 29 \
\text { No Major Flaw } & 60 & 395 \
\hline
\end{array}$
Find the probability that randomly chosen cheese package has no major flaw.
A) 0.79
B) 0.822
C) 0.91
D) 0.21

Accepted Answer

The answer of On a certain day, a cheese packaging...

Question 10

On a recent Saturday, a total of 1112 people visited a local library. Of these people, 266 were under age 10, 496 were aged 10-18, 189 were aged 19-30, and the rest were more than
30 years old.
One person is sampled at random. What is the probability that the person is less than 19 years old?
A) 0.446
B) 0.239
C) 0.685
D) 0.762

Accepted Answer

The probability that a person is less than 19 years old is the sum of those under age 10 and those aged 10-18, which is 266 + 496 = 762. The probability is 762/1112 = 0.685.

Question 11

On a certain day, a cheese packaging facility packaged 490 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major and minor flaws. The following table presents the results.
$\begin{array}{ccc}
\hline & \text { Minor Flaw } & \text { No Minor Flaw } \
\hline \text { Major Flaw } & 16 & 36 \
\text { No Major Flaw } & 63 & 375 \
\hline
\end{array}$
Find the probability that randomly chosen cheese package has a major flaw.
A) 0.106
B) 0.139
C) 0.033
D) 0.073

Accepted Answer

The probability of randomly choosing a cheese package with a major flaw is the number of packages with a major flaw divided by the total number of packages. From the table, we see that there are 16 + 36 = 52 packages with a major flaw, and there are 490 total packages. Therefore, the probability of randomly choosing a cheese package with a major flaw is 52/490 = 0.106.

Question 12

In a recent semester at a local university, 500 students enrolled in both General Chemistry and Calculus I. Of these students, 66 received an A in general chemistry, 73
Received an A in calculus, and 33 received an A in both general chemistry and calculus.
Find the probability that a randomly chosen student received an A in general chemistry or calculus
Or both.
A) 0.278
B) 0.344
C) 0.763
D) 0.212

Accepted Answer

The answer of In a recent semester at a local...

Question 13

On a certain day, a cheese packaging facility packaged 560 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both majo minor flaws. The following table presents the results.
$\begin{array}{ccc}
\hline & \text { Minor Flaw } & \text { No Minor Flaw } \
\hline \text { Major Flaw } & 17 & 39 \
\text { No Major Flaw } & 50 & 454 \
\hline
\end{array}$
Find the probability that randomly chosen cheese package has a flaw (major or minor).
A) 0.811
B) 0.159
C) 0.189
D) 0.22

Accepted Answer

The total number of packages with any flaw is the sum of those with major flaws (17 with minor + 39 without minor = 56), those with minor flaws (17 with major + 50 without major = 67), minus those with both flaws (to avoid double counting) which is 17. So, the total with any flaw is 56 + 67 - 17 = 106. The probability is 106 flawed out of 560 total, which is 106/560 = 0.189.

Question 14

In a recent semester at a local university, 490 students enrolled in both General Chemistry and Calculus I. Of these students, 83 received an A in general chemistry, 86
Received an A in calculus, and 33 received an A in both general chemistry and calculus.
Find the probability that a randomly chosen student did not receive an A in general chemistry.
A) 0.831
B) 0.763
C) 0.169
D) 0.824

Accepted Answer

To find the probability that a student did not receive an A in general chemistry, subtract the number of students who received an A in general chemistry from the total number of students, then divide by the total number of students: (490 - 83) / 490 = 407 / 490 = 0.831.

Question 15

On a certain day, a cheese packaging facility packaged 550 units of mozzarella cheese. Some of these packages had major flaws, some had minor flaws, and some had both major andminor flaws. The following table presents the results.
$\begin{array}{ccc}
\hline & \text { Minor Flaw } & \text { No Minor Flaw } \
\hline \text { Major Flaw } & 23 & 27 \
\text { No Major Flaw } & 59 & 441 \
\hline
\end{array}$
Find the probability that randomly chosen cheese package has a minor flaw.
A) 0.186
B) 0.149
C) 0.107
D) 0.091

Accepted Answer

The answer of On a certain day, a cheese packaging...

Question 16

If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade? 
A) $\frac { 11 } { 26 }$
B) $\frac { 9 } { 26 }$
C) $\frac { 17 } { 52 }$
D) $\frac { 19 } { 52 }$

Accepted Answer

The answer of If one card is drawn from an...

Question 17

Let $E$ be the event that a corn crop has an infestation of ear worms, and let $B$ be the event that a corn crop has an infestation of corn borers.

Suppose that $P ( E ) = 0.29 , P ( B ) = 0.1$, and $P ( E$ and $B ) = 0.09$. Find the probability that a corn crop has no corn borer infestation.
A) 0.3
B) 0.71
C) 0.61
D) 0.9

Accepted Answer

The probability that a corn crop has no corn borer infestation is the complement of the probability that a corn crop has a corn borer infestation, which is $1 - P(B) = 1 - 0.1 = 0.9$.

Question 18

An apartment building has the following distribution of apartments:
$\begin{array}{llll} 
& \mathbf{1} \text { bedroom } & \underline{\text { 2 bedroom }} & \underline{\text { 3 bedroom }} \
\text { 1st floor } & 3 & 1 & 1 \
\text { 2nd floor } & 0 & 4 & 2 \
\text { 3rd floor } & 1 & 4 & 1
\end{array}$ 
If an apartment is selected at random, what is the probability that it is not a 2 bedroom api on the 2nd floor?
A) $\frac { 4 } { 13 }$
B) $\frac { 11 } { 13 }$
C) $\frac { 13 } { 17 }$
D) $\frac { 4 } { 9 }$

Accepted Answer

The answer of An apartment building has the following distribution...

Question 19

On a recent Saturday, a total of 1086 people visited a local library. Of these people, 269 were under age 10, 466 were aged 10-18, 185 were aged 19-30, and the rest were more than
30 years old.
One person is sampled at random. What is the probability that the person is more than 30 years
Old?
A) 0.735
B) 0.153
C) 0.677
D) 0.323

Accepted Answer

The answer of On a recent Saturday, a total of...

Question 20

A poll was taken of 14,499 working adults aged $40 - 70$ to determine their level of educatic The participants were classified by sex and by level of education. The results were as folli
$\begin{array}{cccc}
\hline \text { Education Level } & \text { Male } & \text { Female } & \text { Total } \
\hline \text { High School or Less } & 3157 & 2794 & 5951 \
\text { Bachelor's Degree } & 3723 & 3714 & 7437 \
\text { Master's Degree } & 529 & 482 & 1011 \
\text { Ph.D. } & 50 & 50 & 100 \
\hline \text { Total } & 7459 & 7040 & 14,499
\end{array}$
A person is selected at random. Compute the probability that the person is female and has bachelor's degree.
A) 0.528
B) 0.998
C) 0.256
D) 0.257

Accepted Answer

The answer of A poll was taken of 14,499 working...

Quiz 4: Probability and Counting Rules

Out of 733 items checked out of a public library, 269 were fiction books, 222 were non-fiction books, and 242 were videos (of any genre) . What is the probability that a Randomly-selected item was not a video?

If a single card is drawn from an ordinary deck of cards, what is the probability of drawing a jack, queen, king, or ace?

In a fish tank, there are 15 goldfish, 6 angelfish, and 18 guppies. If a fish is selected at random, find the probability that it is an angelfish or a guppy.

A single card is drawn from a deck. Find the probability of selecting a heart or a 8.

Two dice are rolled. Find the probability of getting doubles or a sum of 2.

On a recent Saturday, a total of 1112 people visited a local library. Of these people, 266 were under age 10, 496 were aged 10-18, 189 were aged 19-30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is less than 19 years old?

If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade?

Let $E$ be the event that a corn crop has an infestation of ear worms, and let $B$ be the event that a corn crop has an infestation of corn borers. Suppose that $P ( E ) = 0.29 , P ( B ) = 0.1$ , and $P ( E$ and $B ) = 0.09$ . Find the probability that a corn crop has no corn borer infestation.

On a recent Saturday, a total of 1086 people visited a local library. Of these people, 269 were under age 10, 466 were aged 10-18, 185 were aged 19-30, and the rest were more than 30 years old. One person is sampled at random. What is the probability that the person is more than 30 years Old?