Assume a company in which you own stock has attracted two takeover offers. Would it ever make sense for your company’s management to favor the lower offer? Does the form of payment affect your answer at all?

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute.

Compute the probability of no arrivals in a one-minute period.

Emergency $911$ calls to a small municipality in Idaho come in at the rate of one every $2$ minutes.
a. What is the expected number of $911$ calls in one hour?
b. What is the probability of three $911$ calls in five minutes?
c. What is the probability of no $911$ calls in a five-minute period?

According to a 2018 article in Esquire magazine, approximately 70% of males over age 70 will develop cancerous cells in their prostate. Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSA) test. However, this test is known to have a high false-positive rate (tests that come back positive for cancer when no cancer is present). Suppose there is a .02 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is .75, and the probability of a false-negative (no indication of cancer when cancer is actually present) is .20.

What is the probability that the male patient has prostate cancer if the PSA test comes back positive?

According to a 2018 article in Esquire magazine, approximately 70% of males over age 70 will develop cancerous cells in their prostate. Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSA) test. However, this test is known to have a high false-positive rate (tests that come back positive for cancer when no cancer is present). Suppose there is a .02 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is .75, and the probability of a false-negative (no indication of cancer when cancer is actually present) is .20.

What is the probability that the male patient has prostate cancer if the PSA test comes back negative?

A financial manager made two new investments—one in the oil industry and one in municipal bonds. After a one-year period, each of the investments will be classified as either successful or unsuccessful. Consider the making of the two investments as an experiment.

How many sample points exist for this experiment?

An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?

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 $P ( D )$.

A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of 7.5 cases involving negligence, and payments were made in one out of every two claims.

What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence?

A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events.

$$\begin{aligned} B & = \text { individual purchased the product } \\ S & = \text { individual recalls seeing the advertisement } \\ B \cap S & = \text { individual purchased the product and recalls seeing the advertisement } \end{aligned}$$

The probabilities assigned were $P ( B ) = .20 , P ( S ) = .40$, and $P ( B \cap S ) = .12$

What is the probability of an individual’s purchasing the product given that the individual recalls seeing the advertisement? Does seeing the advertisement increase the probability that the individual will purchase the product? As a decision maker, would you recommend continuing the advertisement (assuming that the cost is reasonable)?

Let A and B be independent events with P(A) = 0.7 and P(B) = 0.2. Compute (a) P(A ∩ B), (b) P(A ∪ B), and (c) P(A' ∪ B').

A fair coin is tossed four times and comes up tails every time. What is the probability it will come up heads if tossed one more time?

What is the probability that when a fair coin is tossed four times that it comes up heads all four times?

Use the following premerger information about a bidding firm (Firm B) and a target firm (Firm T). Assume that both firms have no debt outstanding.

Firm B has estimated that the value of the synergistic benefits from acquiring Firm T is $9,400.

Question
Are the shareholders of Firm T better off with the cash offer or the stock offer? At what exchange ratio of B shares to T shares would the shareholders in T be indifferent between the two offers?