Question

Please solve the following questions related to Chapter 4: Introduction to Probability.

1. Simon is a general contractor and has submitted two bids for two projects (A and B). The probability of getting project A is 0.54. The probability of getting project B is 0.58. The probability of getting at least one of the projects is 0.87.

a.       What is the probability that she will get both projects?

b.       Are the events of getting the two projects mutually exclusive? Explain, using probabilities.

c.       Are the two events independent? Explain, using probabilities.

Hint: (Please see Chapter 4 – Slides 22 - 23 for definition of union of events, and see Slides 24 - 25 for definition of intersection of events. Please see Slides 26 for Addition Law. Please see Slides 27 for Mutually Exclusively events. Please see Slides 32-33 for Independent events.)

2. Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. In the past, 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 32% of the applicants. Assume events are independent of each other.

a.       What is the probability that you will be accepted in both universities?

b.       What is the probability that you will be accepted to at least one graduate program?

c.       What is the probability that neither university will accept you?

Answer 1