#
Question : A hospital reports that two patients have been admitted who have contracted Crohn's disease : 2150398

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

29) Probabilities of different types of vehicle-to-vehicle accidents are shown below:

Accident Probability

Car to Car 0.52

Car to Truck 0.17

Truck to Truck 0.31

Find the probability that an accident involves a car.

A) 0.52

B) 0.69

C) 0.31

D) 0.17

30) A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.).

Find the probability that both patients survive.

A) 0.24

B) 0.20

C) 0.3136

D) 0.56

31) A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.).

Find the probability that at least one of the patients does not survive.

A) 0.12

B) 0.41

C) 0.30

D) 0.11

32) A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:

Find the probability that a randomly selected piece is either yellow or orange in color.

A) 0.10

B) 10

C) 20

D) 0.20

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

33) A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.).

153) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below:

Educational Background

What is the probability that a randomly chosen manager is either a good managers or has an advanced degree?

A) (159/160)

B) (83/160)

C) (41/80)

D) (1/160)

172) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below:

Educational Background

Given that a manager is rated as fair, what is the probability that this manager has no college background?

A) (2/15)

B) (2/87)

C) (5/8)

D) (1/80)

173) Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below:

Number of Vehicles Involved

Given that an accident involved multiple vehicles, what is the probability that it involved alcohol?

A) (17/400)

B) (110/311)

C) (17/42)

D) (11/40)

174) A researcher investigated whether a student's seat preference was related in any way to the gender of the student. The researcher divided a lecture room into three sections (1-front, middle of the room, 2-front, sides of the classroom, and 3-back of the classroom, both middle and sides) and noted where each student sat on a particular day of the class. The researcher's summary table is provided below.

Suppose a person sitting in the front, middle portion of the class is randomly selected to answer a question. Find the probability that the person selected is female.

A) (5/36)

B) (9/13)

C) (10/39)

D) (10/27)

175) The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of each car and its make (foreign or domestic):

Age of Car (in years)

A car was randomly selected from the lot. Given that the car selected was a foreign car, what is the probability that it was older than 2 years old?

A) (8/23)

B) (3/5)

C) (2/5)

D) (12/23)

**Solve the problem.**

202) A human gene carries a certain disease from a mother to her child with a probability rate of 0.55. That is, there is a 55% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections, or lack thereof, are independent of one another. Find the probability that all four of the children get the disease from their mother.

A) 0.041

B) 0.908

C) 0.05

D) 0.092

203) A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.92, P(C) = 0.9, and P(D) = 0.98. Find the probability that the machine works properly.

A) 0.7618

B) 0.8114

C) 0.2535

D) 0.7465

204) Suppose a basketball player is an excellent free throw shooter and makes 92% of his free throws (i.e., he has a 92% chance of making a single free throw). Assume that free throw shots are independent of one another. Find the probability that the player will make five consecutive free throws.

A) 0.3409

B) 0.6591

C) 1

D) 0

205) Suppose a basketball player is an excellent free throw shooter and makes 90% of his free throws (i.e., he has a 90% chance of making a single free throw). Assume that free throw shots are independent of one another. Find the probability that the player misses three consecutive free throws.

A) 0.271

B) 0.999

C) 0.729

D) 0.001

212) A human gene carries a certain disease from a mother to her child with a probability rate of 0.60. That is, there is a 60% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections, or lack thereof, are independent of one another. Find the probability that none of the children get the disease from their mother.

213) Suppose there is a 32% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in three independent risky stocks. What is the probability that all three stocks end up in total losses?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

227) Classify the events as dependent or independent: Events A and B where P(A) = 0.5, P(B) = 0.7, and P(A and

B) = 0.35.

A) dependent

B) independent

228) Classify the events as dependent or independent: Events A and B where P(A) = 0.2, P(B) = 0.4, and P(A and B) = 0.07.

A) dependent

B) independent