Croq Pain
BUS 260
Homework 2 Solutions
Due before the start of class, Wednesday January 16.
1. 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?
There are two mutually exclusive ways that it could end up being sunny on Wednesday.
P(Sunny Wednesday) = P(Sunny Tuesday AND Sunny Wednesday) + P(Cloudy Tuesday AND Sunny
Wednesday)
Since the weather on consecutive days is related, we use the 4th law:
P(Sunny Tuesday AND Sunny Wednesday) = P(Sunny Tuesday) * P(Sunny Wednesday | Sunny
Tuesday)
= .30 * .60 = .18
Similarly,
P(Cloudy Tuesday and Sunny Wednesday) = P(Cloudy Tuesday) * P(Sunny Wednesday | Cloudy
Tuesday)
= 0.70 * 0.30 = 0.21
So, P(Sunny Wednesday) = .18 + .21 = .39. There’s a 39% chance that it will be sunny on Wednesday.
b) What is the probability that it will be sunny on both Tuesday and Wednesday?
We calculated this while solving part (a). The probability that both days will be sunny is 0.18.
c) It turns out to be sunny on Wednesday. What is the probability that it was also sunny on Tuesday?
Since we know it was sunny on Wednesday, we want to calculate the conditional probability:
P(Sunny on Tuesday | Sunny on Wednesday)
Using the 4th law,
= P(Sunny on Tuesday AND Sunny on Wednesday) / P(Sunny on Wednesday)
= .18/39 = .46. There’s a 46% chance that it was sunny on Tuesday.
2. 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?
Events J and
Homework 2 Solutions
Due before the start of class, Wednesday January 16.
1. 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?
There are two mutually exclusive ways that it could end up being sunny on Wednesday.
P(Sunny Wednesday) = P(Sunny Tuesday AND Sunny Wednesday) + P(Cloudy Tuesday AND Sunny
Wednesday)
Since the weather on consecutive days is related, we use the 4th law:
P(Sunny Tuesday AND Sunny Wednesday) = P(Sunny Tuesday) * P(Sunny Wednesday | Sunny
Tuesday)
= .30 * .60 = .18
Similarly,
P(Cloudy Tuesday and Sunny Wednesday) = P(Cloudy Tuesday) * P(Sunny Wednesday | Cloudy
Tuesday)
= 0.70 * 0.30 = 0.21
So, P(Sunny Wednesday) = .18 + .21 = .39. There’s a 39% chance that it will be sunny on Wednesday.
b) What is the probability that it will be sunny on both Tuesday and Wednesday?
We calculated this while solving part (a). The probability that both days will be sunny is 0.18.
c) It turns out to be sunny on Wednesday. What is the probability that it was also sunny on Tuesday?
Since we know it was sunny on Wednesday, we want to calculate the conditional probability:
P(Sunny on Tuesday | Sunny on Wednesday)
Using the 4th law,
= P(Sunny on Tuesday AND Sunny on Wednesday) / P(Sunny on Wednesday)
= .18/39 = .46. There’s a 46% chance that it was sunny on Tuesday.
2. 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?
Events J and