Question 1

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-A bag contains 7 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue?

Accepted Answer

The total number of marbles is 7 (red) + 4 (blue) + 1 (green) = 12. The probability of not choosing a blue marble is the number of non-blue marbles (7 red + 1 green = 8) divided by the total number of marbles, which is $\frac{8}{12} = \frac{2}{3}$.

Question 2

Solve the problem.
-Find the odds against drawing a heart when a card is drawn at random from a normal deck of 52 playing cards.

Accepted Answer

The odds against drawing a heart from a standard deck of 52 cards are calculated by comparing the number of ways not to draw a heart (39 non-heart cards) to the number of ways to draw a heart (13 heart cards), which gives us 39:13 or simplified to 3:1.

Question 3

Solve the problem.
-Find the odds for getting two tails and a head when three fair coins are flipped.

Accepted Answer

The total number of outcomes when flipping three coins is 2^3 = 8. The favorable outcomes for getting two tails and one head are TTH, THT, and HTT, which are 3 outcomes. Therefore, the odds are 3 favorable outcomes to 5 unfavorable outcomes (8 total outcomes - 3 favorable outcomes).

Question 4

Find the indicated probability.
-A die is rolled 100 times with the following results. $\begin{array} { l | r r r r r r } 
\text { Outcome } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Frequency } & 9 & 25 & 24 & 21 & 9 & 12
\end{array}$
 Compute the empirical probability that the die comes up 2 or 3.

Accepted Answer

The empirical probability of an event is calculated by dividing the number of times the event occurs by the total number of trials. Here, the die comes up 2 or 3 a total of $25 + 24 = 49$ times out of 100 rolls, so the empirical probability is $\frac{49}{100}$.

Question 5

Solve the problem. Round your answer to 5 decimal places when necessary.
-The table shows the leading causes of death for one country in a single recent year.  Assume a population of 86.5 million. How much greater is the risk of death by heart disease than the risk of death by stroke?

Accepted Answer

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

Question 6

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-What is the probability of not rolling a number larger than 4 with a fair die?

Accepted Answer

A fair die has six faces, numbered 1 through 6. Not rolling a number larger than 4 means rolling a 1, 2, 3, or 4, which are 4 out of the 6 possible outcomes. Therefore, the probability is $\frac{4}{6}$, which simplifies to $\frac{2}{3}$.

Question 7

Solve the problem.
-How many different 4-letter sequences can be made using the first 11 letters of the alphabet? Assume that repetition of letters is allowed.

Accepted Answer

Since repetition is allowed, each of the 4 positions in the sequence can be filled by any of the 11 letters. Therefore, the total number of sequences is 11^4 = 14,641.

Question 8

Solve the problem.
-Find the odds for getting two heads when two fair coins are flipped.

Accepted Answer

The total number of outcomes when flipping two coins is 4 (HH, HT, TH, TT). Only one of these outcomes is two heads (HH), so the odds against getting two heads are 3 to 1, which means the odds for getting two heads are 1 to 3.

Question 9

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-What is the probability that 4 randomly selected people all have different birthdays?

Accepted Answer

The probability that 4 randomly selected people all have different birthdays is calculated using the formula for the probability of no shared birthdays: (365/365) * (364/365) * (363/365) * (362/365) = 0.983644087, which rounds to 0.9836.

Question 10

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.07. Find the probability that the region will be hit by a hurricane in 3 consecutive years.

Accepted Answer

The probability of the region being hit by a hurricane in 3 consecutive years is found by multiplying the probability of it happening each year, which is $0.07 \times 0.07 \times 0.07 = 0.000343$.

Question 11

Evaluate the factorial expression.
-$9 !$

Accepted Answer

The factorial of 9 (denoted as 9!) is the product of all positive integers from 1 to 9, which is 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 = 362,880.

Question 12

Solve the problem. Round your answer to 5 decimal places when necessary.
-The table shows the leading causes of death for one country in a single recent year. $\begin{array}{l|r}
{\text { Cause of Death }} & \text { Deaths } \
\hline \text { Heart Disease } & 152,250 \
\text { Cancer } & 116,000 \
\text { AIDS } & 71,775 \
\text { Stroke } & 42,050 \
\text { Pulmonary Disease } & 40,745 \
\text { Accidents } & 30,450 \
\text { Diabetes } & 17,545 \
\text { Pneumonia } & 16,240 \
\text { Kidney Disease } & 8555
\end{array}$ Assume a population of 72.5 million. What is the empirical probability of death by stroke during a single year?

Accepted Answer

The empirical probability of death by stroke is calculated by dividing the number of deaths by stroke (42,050) by the total population (72.5 million). This gives $ \frac{42,050}{72,500,000} = 0.00058 $.

Question 13

Use the at least once rule to find the indicated probability.
-Find the probability of at least one club when you draw cards from a standard deck 17 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from.

Accepted Answer

The probability of drawing at least one club in 17 draws with replacement is found by subtracting the probability of drawing no clubs at all from 1. The probability of not drawing a club in a single draw is 39/52 (since there are 39 non-club cards out of 52 total cards). For 17 independent draws, this probability is (39/52)^17. Therefore, the probability of drawing at least one club is 1 - (39/52)^17, which is approximately 0.992.

Question 14

Solve the problem. Round your answer to 2 decimal places when necessary.
-A country with a population of 103 million has 19,261 traffic fatalities. Find the fatality rate in deaths per 100,000 population.

Accepted Answer

The fatality rate is calculated as (19,261 fatalities / 103,000,000 population) * 100,000 = 18.7 deaths per 100,000 people.

Question 15

Solve the problem.
-Find the odds for drawing an ace when a card is drawn at random from a normal deck of 52 playing cards.

Accepted Answer

The answer of Solve the problem.
-Find the odds for drawing...

Question 16

Find the expected value.
-Experience shows that a ski lodge will be full (199 guests)if there is a heavy snow fall in December, while only partially full (57 guests)with a light snow fall. What is the expected number of guests if
The probability for a heavy snow fall is .40? Assume that heavy snowfall and light snowfall are the
Only two possibilities.

Accepted Answer

The answer of Find the expected value.
-Experience shows that a...

Question 17

Solve the problem. Round your answer to 2 decimal places when necessary.
-A certain U.S. city had 54 traffic fatalities last year. There were 3.3 million miles driven in the city.. Determine the traffic fatality rate per 1,000,000 miles driven.

Accepted Answer

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

Question 18

Solve the problem.
-There are 7 finalists in a singing competition. If a person guesses randomly the top three winners (in any order), what is the probability that they Will guess correctly?

Accepted Answer

The number of ways to choose 3 winners from 7 finalists is given by the combination formula $\binom{7}{3} = 35$. Since there is only 1 correct combination, the probability is $\frac{1}{35}$.

Question 19

Solve the problem.
-There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

Accepted Answer

The answer of Solve the problem.
-There are 5 members on...

Question 20

Find the expected value.
-In a large casino, the house wins on one of its games with a probability of 51,000%. All bets are 1 : 1 . If you win, you gain the amount you bet; if you lose, you lose the amount you bet.
If patrons bet a total of $900,000 on this game in one evening, how much should the casino expect
To earn?

Accepted Answer

The answer of Find the expected value.
-In a large casino,...

Quiz 7: Probability: Living With the Odds

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A bag contains 7 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue?

Solve the problem. -Find the odds against drawing a heart when a card is drawn at random from a normal deck of 52 playing cards.

Solve the problem. -Find the odds for getting two tails and a head when three fair coins are flipped.

Find the indicated probability. -A die is rolled 100 times with the following results. $\begin{array} { l | r r r r r r } \text { Outcome } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Frequency } & 9 & 25 & 24 & 21 & 9 & 12\end{array}$ Compute the empirical probability that the die comes up 2 or 3.

Solve the problem. Round your answer to 5 decimal places when necessary. -The table shows the leading causes of death for one country in a single recent year. Assume a population of 86.5 million. How much greater is the risk of death by heart disease than the risk of death by stroke?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -What is the probability of not rolling a number larger than 4 with a fair die?

Solve the problem. -How many different 4-letter sequences can be made using the first 11 letters of the alphabet? Assume that repetition of letters is allowed.

Solve the problem. -Find the odds for getting two heads when two fair coins are flipped.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -What is the probability that 4 randomly selected people all have different birthdays?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.07. Find the probability that the region will be hit by a hurricane in 3 consecutive years.

Evaluate the factorial expression. - $9 !$

Use the at least once rule to find the indicated probability. -Find the probability of at least one club when you draw cards from a standard deck 17 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from.

Solve the problem. Round your answer to 2 decimal places when necessary. -A country with a population of 103 million has 19,261 traffic fatalities. Find the fatality rate in deaths per 100,000 population.

Solve the problem. -Find the odds for drawing an ace when a card is drawn at random from a normal deck of 52 playing cards.

Solve the problem. Round your answer to 2 decimal places when necessary. -A certain U.S. city had 54 traffic fatalities last year. There were 3.3 million miles driven in the city.. Determine the traffic fatality rate per 1,000,000 miles driven.

Solve the problem. -There are 7 finalists in a singing competition. If a person guesses randomly the top three winners (in any order) , what is the probability that they Will guess correctly?

Solve the problem. -There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?