Posted: May 11th, 2021

1) The electric car company Tesla is working to put its new Model X into production. Whether the

Model X goes into production or not will have a significant impact on their profitability. If the Model

X is put into production next year, there’s an 80% chance that Tesla will be profitable. Otherwise, if the

Model X is not put into production next year there’s only a 5% chance that they will be profitable.

Experts estimate that there is a 25% chance that Tesla will be able to put the Model X into production

next year.

a) If Tesla does put the Model X into production next year, what is the chance that they are not

profitable?

b) What is the probability that Tesla will be profitable next year?

c) It turns out that Tesla is profitable next year. What is the probability that they did put the Model X

into production?

2. In Cook County, each day is either sunny or cloudy. If a day is sunny, the following day will be

sunny with probability 0.60. If a day is cloudy, the following day will be cloudy with probability 0.70.

Suppose it is cloudy on Monday.

a) What is the probability that it will be sunny on Wednesday?

b) What is the probability that it will be sunny on both Tuesday and Wednesday?

3. Elizabeth takes the 85 and 280 freeways to get to campus. Each freeway is either moving or

congested. The 280 is congested 30% of the time. If the 280 is congested, there is an 80% chance that

the 85 is also congested. If the 280 is moving, there is a 20% chance that the 85 is congested.

a) Define events that would be useful in analyzing this situation.

b) Write mathematically the probabilities that are provided above.

c) What is the probability that both freeways are congested?

d) It turns out that the 85 is congested. What is the probability that the 280 is also congested?

4. A job fair was held at the Student Union. 25% of the students who attended received job offers. Of

all of the students at the job fair, 40% were from the College of Business. Among these business

students, 50% received job offers.

Let J be the event that a student is offered a job. Let B be the event that the student is from the College

of Business.

a) Are events J and B independent? Why or why not?

b) Are events J and B mutually exclusive? Why or why not?

c) Joe, who is not a business student, attended the job fair. What is the probability that he received

a job offer?

d) Another student, Samantha, received a job offer. What is the probability that she is a Business

student?

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