Probability Theory

Q1. Nintendo recently developed a new video game. Its market potential is to be tested by 80 veteran game players.

a. What is the experiment?

b. What is one possible outcome?

c. Suppose 65 players tried the new game and said they like it. Is 65 a probability?

d. The probability that the new game will be a success is computed to be -1.0. Comment.

e. Specify one possible event.

Q2. The Board of Trustees of Jose Rizal University consists of 8 men and 4 women. A four-person search committee is to be chosen at random to conduct a university-wide search for a new President.

a. What is the probability all four members of the search committee will be women?

b. What is the probability all four members will be men?

c. Does the sum of the probabilities for the events described in (a) and (b) equal 1? Explain.

Q3. In 2020, at Nestle Corporation, 200 people had colds during the year. One hundred fifty-five people who did no exercising had colds, and the remainder of the people with colds were involved in a weekly exercise program. Half of the 1,000 employees were involved in some type of exercise.

a. What is the probability that an employee will have a cold next year?

b. Given that an employee is involved in an exercise program, what is the probability of getting a cold next year?

c. What is the probability that an employee that is not involved in an exercise program will get a cold next year?

d. Are exercising and getting a cold, independent events? Explain your answer.

Q4. The Zhejiang Golden Bulls (ZGB), a professional basketball team has won 12 of its last 20 games and is expected to continue winning at the same percentage rate. The team's ticket manager is anxious to attract a large crowd to tomorrow's game against the Shanxi Loongs (SL) but believes that depends on how the ZGB perform tonight against the Liaoning Flying Leopards (LFL). He assesses the probability of drawing a large crowd to be 0.90 should the team win tonight. What is the probability that the ZGB wins against LFL and that there will be a large crowd at tomorrow's game against SL?