Question 1

Find the indicated probability.
-A bag contains 8 red marbles, 4 blue marbles, and 1 green marble. Find P(not blue).

A) 9

B) $\frac { 4 } { 13 }$

C) $\frac { 13 } { 9 }$

D) $\frac { 9 } { 13 }$

Accepted Answer

The probability of not drawing a blue marble is the number of non-blue marbles divided by the total number of marbles. There are 8 red and 1 green marble, making 9 non-blue marbles out of a total of 13 marbles. Thus, P(not blue) = 9/13.

Question 2

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
-The following table contains data from a study of two airlines which fly to Small Town, USA. $$\begin{array} { c | c c } 
& \text { Number of flights } & \text { Number of flights } \
& \text { which were on time } & \text { which were late } \
\hline \text { Podunk Airlines } & 33 & 6 \
\text { Upstate Airlines } & 43 & 5
\end{array}$$ 
If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time given that it was an Upstate Airlines flight.

A) $\frac { 43 } { 87 }$

B) $\frac { 43 } { 48 }$

C) $\frac { 11 } { 76 }$

D) None of the above is correct.

Accepted Answer

The probability that a flight was on time given it was an Upstate Airlines flight is the number of on-time Upstate Airlines flights divided by the total number of Upstate Airlines flights: $ \frac{43}{43+5} = \frac{43}{48} $.

Question 3

Find the indicated probability.
-A class consists of 79 women and 33 men. If a student is randomly selected, what is the probability that the student is a woman?

A) $\frac { 79 } { 112 }$

B) $\frac { 1 } { 112 }$

C) $\frac { 33 } { 112 }$

D) $\frac { 79 } { 33 }$

Accepted Answer

The probability of selecting a woman is the number of women divided by the total number of students: $\frac{79}{79+33} = \frac{79}{112}$.

Question 4

Swinging Sammy Skor's batting prowess was simulated to get an estimate of the probability that Sammy will get a hit. Let $1 =$ HIT and $0 =$ OUT. The output from the simulation was as follows.

$\begin{array}{llcc}
1&0&0&0&1&0&0&1&0&0&1&1&1&1&0&0&0&0&1&1&1&1&0&0&0&0&0&1&1&0&0&1&1&1&1&0&0&0&0&0&0&1&1&1&1&1
\end{array}$

Estimate the probability that he gets a hit.
A) 0.301
B) 0.286
C) 0.476
D) 0.452

Accepted Answer

The probability is estimated by dividing the number of hits (1s) by the total number of attempts. There are 20 hits out of 42 attempts, so the probability is 20/42 ≈ 0.476.

Question 5

Refer to the table which summarizes the results of testing for a certain disease. 
$\begin{array}{l|cc}
&\text {  Positive Test Result}&\text {  Negative Test Result }\
\hline \text { Subject has the disease } & 82 & 10 \
\text { Subject does not have the disease } & 25 & 326
\end{array}$

A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative?
A) 0.109
B) 0.208
C) 0.03
D) 0.97

Accepted Answer

The probability that the subject has the disease given a negative test result is calculated as the number of true negatives (10) divided by the total number of negative test results (10 + 326), which is 10/336 = 0.03.

Question 6

A musician plans to perform 4 selections. In how many ways can she arrange the musical selections?
A) 4
B) 16
C) 120
D) 24

Accepted Answer

The number of ways to arrange 4 selections is 4! (4 factorial), which is 4 x 3 x 2 x 1 = 24.

Question 7

A bin contains 72 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary.
A) 0
B) 0.861
C) 0.522
D) 0.473

Accepted Answer

The answer of A bin contains 72 light bulbs of...

Question 8

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
-If you drew one card from a standard deck, would it be "unusual" to draw a 6?
A) Yes
B) No

Accepted Answer

There are 4 sixes in a standard deck of 52 cards, so the probability of drawing a 6 is 4/52, which simplifies to 1/13 or approximately 0.077. Since 0.077 is greater than 0.05, it is not considered "unusual."

Question 9

In one town, 45% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary.
A) 0.198
B) 0.900
C) 0.203
D) 0.450

Accepted Answer

The answer of In one town, 45% of all voters...

Question 10

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
-Assume that a study of 500 randomly selected school bus routes showed that 483 arrived on time. 
Is it "unusual" for a school bus to arrive late?
A) Yes
B) No

Accepted Answer

The answer of Answer the question, considering an event to...

Question 11

Refer to the table which summarizes the results of testing for a certain disease. 
$$\begin{array} { l | c c } 
& \text { Positive Test Result } & \text { Negative Test Result } \
\hline \text { Subject has the disease } & 87 & 6 \
\text { Subject does not have the disease } & 27 & 158
\end{array}$$
 If one of the results is randomly selected, what is the probability that it is a false positive (test indicates the person has the disease when in fact they don't)? What does this probability suggest about the accuracy of the test?
A) 0.410; The probability of this error is high so the test is not very accurate.
B) 0.146; The probability of this error is high so the test is not very accurate.
C) 0.0216; The probability of this error is low so the test is fairly accurate.
D) 0.0971; The probability of this error is high so the test is not very accurate.

Accepted Answer

The probability of a false positive is calculated as the number of false positives (27) divided by the total number of tests (278), which equals 0.0971. This suggests that the probability of this error is relatively high, indicating the test may not be very accurate.

Question 12

Is Event B dependent or independent of Event A?
-A: A bird lands on your head. 
B: The bird lays an egg.

A) Independent
B) Dependent

Accepted Answer

The answer of Is Event B dependent or independent of...

Question 13

A tourist in France wants to visit 6 different cities. How many different routes are possible?
A) 720
B) 120
C) 6
D) 36

Accepted Answer

The number of different routes is the number of permutations of 6 cities, which is 6! (factorial of 6), equal to 720.

Question 14

Find the indicated probability.
-A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 9 wood and 19 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.
A) 0.545
B) 0.14
C) 0.595
D) There is insufficient information to answer the question.

Accepted Answer

The probability of selecting a wood racket is 100/200 = 0.5. The probability of selecting a defective racket is (9+19)/200 = 0.14. The probability of selecting a wood and defective racket is 9/200 = 0.045. Using the formula P(A or B) = P(A) + P(B) - P(A and B), we get 0.5 + 0.14 - 0.045 = 0.595.

Question 15

Many calculators or computers cannot directly calculate 70 ! or higher. When $\mathrm { n }$ is large, $\mathrm { n }$ ! can be approximated by $n ! = 10 \mathrm {~K}$, where $\mathrm { K } = ( \mathrm { n } + 0.5 ) \log \mathrm { n } + 0.39908993 - 0.43429448 \mathrm { n }$. 
Evaluate 95 ! using the approximation given above.
A) $1.059 \times 10 ^ { 147 }$
B) $1.032 \times 10 ^ { 148 }$
C) $1.087 \times 10 ^ { 394 }$
D) $1.480 \times 10 ^ { 2 }$

Accepted Answer

Using the approximation formula, calculate K for n = 95, then compute 10^K to find the approximate value of 95!.

Question 16

Use Bayes' theorem to find the indicated probability.
-Shameel has a flight to catch on Monday morning. His father will give him a ride to the airport. If it rains, the traffic will be bad and the probability that he will miss his flight is 0.06. If it doesn't rain, The probability that he will miss his flight is 0.02. The probability that it will rain on Monday is 0.29.
Suppose that Shameel misses his flight. What is the probability that it was raining?
A) 0.29
B) 0.551
C) 0.449
D) 0.06

Accepted Answer

P(Rain | Missed flight) = P(Missed flight | Rain) * P(Rain) / P(Missed flight)= 0.06 * 0.29 / (0.06 * 0.29 + 0.02 * 0.71)= 0.551

Question 17

Use Bayes' theorem to find the indicated probability.
-At Sally's Hair Salon there are three hair stylists. 23% of the hair cuts are done by Chris, 32% are done by Karine, and 45% are done by Amy.
Chris finds that when he does hair cuts, 7% of the customers are not satisfied. Karine finds that when she does hair cuts, 8% of the customers are not satisfied.
Amy finds that when she does hair cuts, 3% of the customers are not satisfied.
Suppose that a customer leaving the salon is selected at random. If the customer is not satisfied, what is the probability that their hair was done by Amy?
A) 0.245
B) 0.324
C) 0.03
D) 0.292

Accepted Answer

The probability that a customer is not satisfied with their haircut is:P(not satisfied) = 0.07 * 0.23 + 0.08 * 0.32 + 0.03 * 0.45 = 0.046The probability that a customer's hair was done by Amy given that they are not satisfied is:P(Amy | not satisfied) = P(not satisfied | Amy) * P(Amy) / P(not satisfied)= 0.03 * 0.45 / 0.046 = 0.292

Question 18

Find the indicated probability.
-On a multiple choice test, each question has 3 possible answers. If you make a random guess on the first question, what is the probability that you are correct?
A) 0
B) 3
C) 1
D) $\frac { 1 } { 3 }$

Accepted Answer

There are 3 possible answers, and you are making a random guess, so the probability of being correct is 1/3.

Question 19

Find the indicated probability.
-The table below describes the smoking habits of a group of asthma sufferers. $$\begin{array} { r | c c c r } 
&&  \text { Light }& \text { Heavy }  \
& \text { Nonsmoker } & \text { smoker } & \text { smoker } & \text { Total } \
\hline \text { Men } & 303 & 35 & 37 & 375 \
\text { Women } & 413 & 31 & 45 & 489 \
\text { Total } & 716 & 66 & 82 & 864
\end{array}$$ If two different people are randomly selected from the 864 subjects, find the probability that they are both heavy smokers. Round to six decimal places.
A) 0.001834
B) 0.008908
C) 0.009007
D) 0.0001487

Accepted Answer

The answer of Find the indicated probability.
-The table below describes...

Question 20

Find the indicated complement.
-Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.236. Find the probability that in a given year it will not snow on January 1st in that town.
A) 4.237
B) 0.309
C) 1.236
D) 0.764

Accepted Answer

The probability that it will not snow is the complement of the probability that it will snow. Therefore, it is 1 - 0.236 = 0.764.

Quiz 4: Probability

Find the indicated probability. -A bag contains 8 red marbles, 4 blue marbles, and 1 green marble. Find P(not blue) .

Find the indicated probability. -A class consists of 79 women and 33 men. If a student is randomly selected, what is the probability that the student is a woman?

A musician plans to perform 4 selections. In how many ways can she arrange the musical selections?

A bin contains 72 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary.

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -If you drew one card from a standard deck, would it be "unusual" to draw a 6?

In one town, 45% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary.

Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05. -Assume that a study of 500 randomly selected school bus routes showed that 483 arrived on time. Is it "unusual" for a school bus to arrive late?

Is Event B dependent or independent of Event A? -A: A bird lands on your head. B: The bird lays an egg.

A tourist in France wants to visit 6 different cities. How many different routes are possible?

Find the indicated probability. -A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 9 wood and 19 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.

Find the indicated probability. -On a multiple choice test, each question has 3 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

Find the indicated complement. -Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.236. Find the probability that in a given year it will not snow on January 1st in that town.