Question 1

If a household has at least one cat, there is a 30% probability that the household has at least one dog. Thirty percent of households have at least one cat and 33% of households have at least one dog. Given that a household does not have at least one dog, the probability that the same household does not have at least one cat is --------.

Accepted Answer

To find the probability that a household does not have at least one cat given it does not have at least one dog, we can use the formula for conditional probability. Let's denote C as the event that a household has at least one cat, and D as the event that a household has at least one dog. We are given:- P(C) = 0.30 (probability of having at least one cat)- P(D) = 0.33 (probability of having at least one dog)- P(D|C) = 0.30 (probability of having at least one dog given that the household has at least one cat)We want to find P(C'|D'), where C' and D' are the complements of C and D, respectively, meaning the household does not have a cat or a dog.First, find P(C and D), the probability of a household having both a cat and a dog. Since P(D|C) = 0.30, it means 30% of the 30% of households with cats also have dogs, so:P(C and D) = P(D|C) * P(C) = 0.30 * 0.30 = 0.09.Now, find P(D'), the probability of not having a dog:P(D') = 1 - P(D) = 1 - 0.33 = 0.67.Next, we need to find P(C' and D'), the probability of a household having neither a cat nor a dog. Since we know the probabilities of having a cat, a dog, and both, we can find the probability of having neither by subtracting from 1 the probabilities of having just a cat, just a dog, and both:P(C' and D') = 1 - P(C) - P(D) + P(C and D) = 1 - 0.30 - 0.33 + 0.09 = 0.46.Finally, use the formula for conditional probability to find P(C'|D'):P(C'|D') = P(C' and D') / P(D') = 0.46 / 0.67 ≈ 0.69.Therefore, the correct answer is D) 0.69.

Question 2

According to a survey of business executives, 78% received a pay raise when they asked for one. A random sample of four executives was selected. The probability that all four received a raised when they asked for one is------- .

Accepted Answer

The probability that all four executives received a raise when they asked for one is calculated by multiplying the individual probabilities for each executive, assuming independence. Since 78% (or 0.78) of executives received a raise when they asked, the probability for all four is $0.78^4 = 0.370$.

Question 3

Alison is the chair of a business department that consists of nine full-time faculty. She needs to schedule a meeting with each faculty to review their performance over the past year. The number of different ways these nine faculty can be scheduled is ------- .

Accepted Answer

The number of different ways to schedule meetings with nine faculty members is calculated by finding the factorial of 9, which is 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880.

Question 4

At the beginning of a Major League Baseball season, a panel of sports writers decided that the Los Angeles Dodgers were the most likely team to win the World Series that year. This is an example of using -------- probability.

Accepted Answer

The panel's decision is based on their opinions and judgments rather than on historical data or specific statistical analysis, which is characteristic of subjective probability.

Question 5

The------ states that if there are k1 choices for the first event, k2 choices for the second event, . . ., and kn choices for the nth event, then the total number of possible outcomes are (k1)(k2)(k3). . . (kn).

Accepted Answer

The Fundamental Counting Principle states that if there are multiple events happening in sequence, the total number of outcomes is the product of the number of choices for each event.

Question 6

There are 30 Major League Baseball teams in the National League. Five of these teams will make the playoffs at the end of the season. The number of unique groups of teams that can make the playoffs is ---------.

Accepted Answer

The number of unique groups of teams that can make the playoffs is calculated using the combination formula, which is C(n, r) = n! / [r!(n - r)!], where n is the total number of items (teams in this case), and r is the number of items to choose (teams making the playoffs). Here, n = 30 and r = 5, so the calculation is C(30, 5) = 30! / [5!(30 - 5)!] = 142,506.

Question 7

The probability of winning a 5/25 lottery game where 5 numbers are picked from a range of 25 is ---------.

Accepted Answer

The probability of winning a 5/25 lottery game is calculated by finding the number of ways to choose 5 numbers out of 25, which is a combination problem (denoted as 25C5). The formula for combinations is C(n, r) = n! / [r!(n-r)!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial. For a 5/25 lottery, this is 25! / (5!(25-5)!) = 53,130. Therefore, the probability of winning is 1 out of these 53,130 possible combinations, which is 1/53,130.

Question 8

Which one of the following is not a valid number for a probability?

Accepted Answer

Probabilities are values between 0 and 1 (inclusive), or equivalently, between 0% and 100%. A value of 1.50 (or 150%) is not a valid probability.

Question 9

The probability of the intersection of two events is known as a _______ probability.

Accepted Answer

Joint probability is the probability of two events happening at the same time.

Question 10

Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is ______________.

Accepted Answer

The answer of Ten percent of customers who walk into...

Question 11

According to a recent survey, 38% of U.S. households used only cell phones for their phone service. A random sample of four households was selected. The probability that the first three used only cell phones and the third had a landline is----- .

Accepted Answer

The probability that the first three households use only cell phones is $0.38^3$ and the probability that the fourth household uses a landline (thus not using only cell phones) is $1 - 0.38 = 0.62$. Multiplying these probabilities gives $0.38^3 \times 0.62 = 0.034$.

Question 12

Suppose the Department of Labor reported that there was a 50% probability that the unemployment rate would drop below 8% by the end of the calendar year. This is an example of using ------ probability.

Accepted Answer

Subjective probability is based on personal judgment or opinion rather than on exact calculations or specific past events. The Department of Labor's report of a 50% probability for the unemployment rate dropping is based on expert judgment and analysis, making it a subjective probability.

Question 13

---------- probability requires that you count the frequency that an event occurs through an experiment and calculate the probability from the experiment's relative frequency distribution.

Accepted Answer

Empirical probability is calculated by observing actual experiments or occurrences to determine how frequently an event happens, rather than by theoretical calculation.

Question 14

Which one of the following statements about probability is not true?

Accepted Answer

Mutually exclusive events mean that if one event occurs, the other cannot. It does not guarantee that one of them must occur.

Question 15

After Bill attends the first statistics class of the semester and reads the syllabus, he decides that the most likely grade he will receive for the course is a "B". This is an example of using ------- probability.

Accepted Answer

Subjective probability is based on personal judgment or opinion rather than on exact calculations or specific past events. Bill's prediction of his grade is based on his personal assessment and not on objective data, making it a subjective probability.

Question 16

The Western Athletic Conference (WAC)consists of eight NCAA teams that compete in a variety of sports. The number of different ways these eight teams can finish in the conference standings at the end of the basketball season is --------.

Accepted Answer

The answer of The Western Athletic Conference (WAC)consists of eight...

Question 17

There are 23 golfers participating in a weekend tournament. Prizes are awarded to the first, second, third, and fourth place finishers. The number of different ways these four places can be filled by those playing over the weekend is ------- .

Accepted Answer

The answer of There are 23 golfers participating in a...

Question 18

Craftsman sells 10-digit keypads that are installed on homes to open the garage door. The consumer chooses a 5-number code when programming the keypad. The total number of codes that the consumer can choose from is ______.

Accepted Answer

The consumer can choose each of the 5 digits from 0 to 9, which gives 10 choices per digit. Therefore, the total number of codes is 10^5 = 100,000.

Question 19

The ------- of Events A and B represent the number of instances in which either Event A or Event B or both occur together.

Accepted Answer

The union of Events A and B includes all instances where Event A occurs, Event B occurs, or both events occur together, covering all possibilities of either event happening.

Question 20

Two six-sided die are rolled. The probability of the sum of the two die being a 10 is ------ .

Accepted Answer

The total number of outcomes when rolling two six-sided dice is 36 (6 sides on the first die times 6 sides on the second die). The combinations that sum to 10 are (4,6), (5,5), and (6,4), totaling 3 combinations. Therefore, the probability is 3/36 = 1/12, which equals approximately 0.083.

Quiz 4: Relationships and Sexuality