Better at Getting Deals. To better understand how husbands and wives feel about their finances, Money magazine conducted a national poll of 1,010 married adults age 25 and older with household incomes of $\$ 50,000$ or more (Money website). Consider the following example set of responses to the question, "Who is better at getting deals?"

$$\begin{aligned} &\text { Who Is Better? }\\ &\begin{array}{lccc} \text { Respondent } & \text { I Am } & \text { My Spouse } & \text { We Are Equal } \\ \text { Husband } & 278 & 127 & 102 \\ \text { Wife } & 290 & 111 & 102 \end{array} \end{aligned}$$

a. Develop a joint probability table and use it to answer the following questions.

Better at Getting Deals. To better understand how husbands and wives feel about their finances, Money magazine conducted a national poll of 1,010 married adults age 25 and older with household incomes of $\$ 50,000$ or more (Money website). Consider the following example set of responses to the question, "Who is better at getting deals?"

$$\begin{aligned} &\text { Who Is Better? }\\ &\begin{array}{lccc} \text { Respondent } & \text { I Am } & \text { My Spouse } & \text { We Are Equal } \\ \text { Husband } & 278 & 127 & 102 \\ \text { Wife } & 290 & 111 & 102 \end{array} \end{aligned}$$

c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife?

Better at Getting Deals. To better understand how husbands and wives feel about their finances, Money magazine conducted a national poll of 1,010 married adults age 25 and older with household incomes of $\$ 50,000$ or more (Money website). Consider the following example set of responses to the question, "Who is better at getting deals?"

$$\begin{aligned} &\text { Who Is Better? }\\ &\begin{array}{lccc} \text { Respondent } & \text { I Am } & \text { My Spouse } & \text { We Are Equal } \\ \text { Husband } & 278 & 127 & 102 \\ \text { Wife } & 290 & 111 & 102 \end{array} \end{aligned}$$

d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband?

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. The University of Pennsylvania received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, Penn has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375 (USA Today, January 24, 2001). Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.

Use the data to estimate $P ( E )$ , $P ( R )$ , and $P ( D )$.

To better understand how husbands and wives feel about their finances, Money magazine conducted a national poll of 1010 married adults age 25 and older with household incomes of $50,000 or more (Money website). Consider the following example set of responses to the question, “Who is better at getting deals?”

Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. The University of Pennsylvania received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, Penn has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375 (USA Today, January 24, 2001). Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.

Are events $E$ and $D$ mutually exclusive? Find $P ( E \cap D )$.

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. The University of Pennsylvania received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, Penn has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375 (USA Today, January 24, 2001). Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.

For the 2375 students admitted to Penn, what is the probability that a randomly selected student was accepted during early admission?

Assume that we have two events, $A$ and $B ,$ that are mutually exclusive. Assume further that we know $P ( A ) = .30$ and $P ( B ) = .40$ .

What is $P ( A | B ) ?$

Ivy League Admissions. High school seniors with strong academic records apply to the nation's most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. Suppose that for a recent admissions class, an Ivy League college received 2,851 applications for early admission. Of this group, it admitted 1,033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted $18 \%$ of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375 . Let $E, R$, and $D$ represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.

d. Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

Assume that we have two events, $A$ and $B,$ that are mutually exclusive. Assume further that we know $P ( A ) = .30$ and $P ( B ) = .40$ .

What is $P ( A \cap B ) ?$

A consulting firm submitted a bid for a large research project. The firm’s management initially felt they had a 50–50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 75% of the successful bids and 40% of the unsuccessful bids the agency requested additional information.

What is the prior probability of the bid being successful (that is, prior to the request for additional information)?

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. The University of Pennsylvania received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, Penn has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375 (USA Today, January 24, 2001). Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.

Suppose a student applies to Penn for early admission. What is the probability the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

A jewelry maker wants to survey a sample of Davis County high school seniors in order to determine preferences for class rings. Which procedure would be most appropriate for obtaining a sample of Davis County high school seniors? a. Mail surveys to a random sample of Davis County high school students. b. Randoml y select an assortment of classes for seniors at each Davis County high school and distribute surveys to the students in those classes. c. Randomly select an assortment of Davis County high school teachers and distribute surveys to them. d. Distribute surveys to all Davis County high school seniors on the honor roll.

company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 6% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 5% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.

What percentage of the employees will experience lost-time accidents in both years?