Question 1

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-An IRS auditor randomly selects 3 tax returns from 50 returns of which 5 contain errors. What is the probability that she selects none of those containing errors?

Accepted Answer

The probability of selecting none of the returns with errors can be calculated using combinations. There are 45 returns without errors out of 50. The number of ways to choose 3 returns from these 45 is 45C3. The total number of ways to choose any 3 returns from the 50 is 50C3. The probability is the ratio of these two combinations: (45C3) / (50C3) ≈ 0.724.

Question 2

Use the at least once rule to find the indicated probability.
-Find the probability of at least one queen when you draw cards from a standard deck 11 times; assume you replace the card each time you draw , so there are always 52 cards to draw from.

Accepted Answer

The answer of Use the at least once rule to...

Question 3

Find the expected value.
-An insurance company will insure a $220,000 home for its total value for an annual premium of $590. If the company spends $30 per year to service such a policy, the probability of total loss for
Such a home in a given year is 0.001 and you assume either total loss or no loss will occur, what is
The company's expected annual gain (or profit)on each such policy?

Accepted Answer

The answer of Find the expected value.
-An insurance company will...

Question 4

Solve the problem.
-A local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors. The other sizes come in 2 colors. How many choices of carpet are there?

Accepted Answer

The answer of Solve the problem.
-A local department store sells...

Question 5

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-If you are dealt two cards successively (with replacement of the first)from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

Accepted Answer

The probability of drawing a heart from a 52-card deck is $\frac{13}{52}$ or $\frac{1}{4}$, and the probability of drawing a diamond, also from a 52-card deck, is $\frac{13}{52}$ or $\frac{1}{4}$. Since the draws are independent (the card is replaced), the combined probability is $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$.

Question 6

Use the at least once rule to find the indicated probability.
-A study conducted at a certain college shows that 64% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected
Graduates, at least one finds a job in his or her chosen field within a year of graduating.

Accepted Answer

The probability that a randomly selected graduate finds a job in their chosen field within a year of graduating is 0.64. The probability that a randomly selected graduate does not find a job in their chosen field within a year of graduating is 0.36. The probability that none of the 5 randomly selected graduates finds a job in their chosen field within a year of graduating is 0.36^5 = 0.0102. The probability that at least one of the 5 randomly selected graduates finds a job in their chosen field within a year of graduating is 1 - 0.0102 = 0.994.

Question 7

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.441. Find the probability that in a given year it will not snow on January 1st in that town.

Accepted Answer

The probability that it will not snow is 1 minus the probability that it will snow, which is 1 - 0.441 = 0.559.

Question 8

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is greater than 10?

Accepted Answer

There are 36 possible outcomes when rolling two 6-sided dice. The sums greater than 10 are 11 and 12. The combinations for these sums are (5,6), (6,5), and (6,6), totaling 3 outcomes. Thus, the probability is 3/36 = 1/12.

Question 9

Find the indicated probability.
-The following table show the results of a clinical trial for an allergy drug. $$\begin{array} { l | c | c | c | c } 
& \begin{array} { c } 
\text { Allergy } \
\text { drug }
\end{array} & \text { Placebo } & \begin{array} { c } 
\text { Control } \
\text { (no treatment) }
\end{array} & \text { Total } \
\hline \text { Improvement } & 145 & 85 & 41 & 271 \
\text { No improvement } & 55 & 115 & 59 & 229 \
\text { Total } & 200 & 200 & 100 & 500
\end{array}$$ What is the probability that a randomly selected person was given a placebo or improved? Round your answer to the nearest thousandth when necessary.

Accepted Answer

The probability that a randomly selected person was given a placebo or improved is found by adding the number of people who were given a placebo (200) to the number of people who improved (271), and then subtracting the overlap (those who were given a placebo and improved, which is 85) to avoid double-counting. This gives us $200 + 271 - 85 = 386$. Then, we divide by the total number of people (500) to find the probability: $386 / 500 = 0.772$.

Question 10

Decide whether events A and B are overlapping or non-overlapping.
-A card is drawn at random from a deck of cards. Event A is that the card selected is a queen and event B is that the card selected is a two.

Accepted Answer

Events A and B are non-overlapping because a card cannot be both a queen and a two at the same time.

Question 11

Find the indicated probability.
-The following table displays the number of siblings for students at one middle school. Find the probability that a randomly selected student in the school has 2 siblings. Round your answer to the
Nearest thousandth. $$\begin{array} { c | c } 
\begin{array} { l } 
\text { Number } \
\text { of siblings }
\end{array} & \text { Frequency } \
\hline 0 & 189 \
1 & 246 \
2 & 124 \
3 & 58 \
4 & 25 \
5 & 10 \
6 & 6 \
7 & 3
\end{array}$$

Accepted Answer

The probability is calculated by dividing the frequency of students with 2 siblings (124) by the total number of students (661). 124/661 ≈ 0.188.

Question 12

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen.

Accepted Answer

The probability of drawing a king first is $\frac{4}{52}$ since there are 4 kings in a deck of 52 cards. After drawing a king, there are 51 cards left, and the probability of drawing a queen next is $\frac{4}{51}$ because there are 4 queens in the remaining deck. Multiplying these probabilities gives the overall probability: $\frac{4}{52} \times \frac{4}{51} = \frac{1}{13} \times \frac{4}{51} = \frac{4}{663}$.

Question 13

Evaluate the factorial expression.
-$\frac { 4 ! } { 2 ! }$

Accepted Answer

The factorial expression $\frac{4!}{2!}$ simplifies to $\frac{4 \times 3 \times 2 \times 1}{2 \times 1}$, which equals $4 \times 3 = 12$.

Question 14

Solve the problem.
-The table shows the prizes and probabilities of winning (on a single $1 ticket)for a particular state lottery.  How much would you expect to win or lose if you bought one $1 ticket every day for a year?
Round to the nearest dollar.

Accepted Answer

The answer of Solve the problem.
-The table shows the prizes...

Question 15

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary.
-Every week, Joe plays chess with his father. Of the last 50 games, Joe has won 60% of the games. What is the probability that Joe will win the next game?

Accepted Answer

The relative frequency method estimates the probability of an event by dividing the number of times the event has occurred by the total number of trials. Joe has won 60% of the last 50 games, so the probability of him winning the next game, based on past performance, is 0.60.

Question 16

Solve the problem.
-A shoe store carries one brand of shoe in 5 different styles, 5 sizes, and 3 colors. How many different shoes are available of this one brand?

Accepted Answer

The answer of Solve the problem.
-A shoe store carries one...

Question 17

Solve the problem. Round your answer to 2 decimal places when necessary.
-In a recent year, there were 62 accidents in commercial aviation among major airlines over 15.5 million flight hours. Find the accident rate in units of accidents per 100,000 flight hours.

Accepted Answer

The answer of Solve the problem. Round your answer to...

Question 18

Use the at least once rule to find the indicated probability.
-The probability of winning $20 in a particular lottery is 0.04. What is the probability that you will get at least one $20 winner if you buy 90 tickets?

Accepted Answer

The probability of not winning $20 on a single ticket is 1 - 0.04 = 0.96. The probability of not winning on any of the 90 tickets is 0.96^90. Therefore, the probability of winning at least once is 1 - 0.96^90, which is approximately 0.975.

Question 19

Evaluate the factorial expression.
-$\frac { 10 ! } { 3 ! 7 ! }$

Accepted Answer

The expression simplifies to $ \frac{10 \times 9 \times 8 \times 7!}{3 \times 2 \times 1 \times 7!} $, where the $7!$ cancels out, leaving $ \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120$.

Question 20

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-A fair die is rolled. What is the probability of rolling a 3 or a 4?

Accepted Answer

The probability of rolling a 3 or a 4 on a fair die is $\frac{2}{6}$ because there are 2 favorable outcomes (rolling a 3 or a 4) out of 6 possible outcomes (1 through 6 on the die), which simplifies to $\frac{1}{3}$.

Quiz 7: Probability: Living With the Odds

Find the indicated probability. Round your answer to 6 decimal places when necessary. -An IRS auditor randomly selects 3 tax returns from 50 returns of which 5 contain errors. What is the probability that she selects none of those containing errors?

Use the at least once rule to find the indicated probability. -Find the probability of at least one queen when you draw cards from a standard deck 11 times; assume you replace the card each time you draw , so there are always 52 cards to draw from.

Solve the problem. -A local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors. The other sizes come in 2 colors. How many choices of carpet are there?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.441. Find the probability that in a given year it will not snow on January 1st in that town.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is greater than 10?

Decide whether events A and B are overlapping or non-overlapping. -A card is drawn at random from a deck of cards. Event A is that the card selected is a queen and event B is that the card selected is a two.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen.

Evaluate the factorial expression. - $\frac { 4 ! } { 2 ! }$

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. -Every week, Joe plays chess with his father. Of the last 50 games, Joe has won 60% of the games. What is the probability that Joe will win the next game?

Solve the problem. -A shoe store carries one brand of shoe in 5 different styles, 5 sizes, and 3 colors. How many different shoes are available of this one brand?

Solve the problem. Round your answer to 2 decimal places when necessary. -In a recent year, there were 62 accidents in commercial aviation among major airlines over 15.5 million flight hours. Find the accident rate in units of accidents per 100,000 flight hours.

Use the at least once rule to find the indicated probability. -The probability of winning $20 in a particular lottery is 0.04. What is the probability that you will get at least one $20 winner if you buy 90 tickets?

Evaluate the factorial expression. - $\frac { 10 ! } { 3 ! 7 ! }$

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A fair die is rolled. What is the probability of rolling a 3 or a 4?