1. Suppose during the first die roll event A is getting a 4. Which of the following events are independent of event A? Explain why or why not.
a) Rolling a second die and getting a four
b) Rolling the first die and getting a six
c) Rolling the first die and getting an even number
2. The probability of a computer having a virus within a company is equal to 0.02. What is the probability that 5 randomly chosen computers will all be free of viruses (none of the 5 computers have viruses)? You may assume independence.
3. The top three foul shooters on the women's basketball UConn 2013-2014 season were KiahStokes and Moriah Jefferson and Stefanie Dolson with foul shooting percentages of 0.600, 0.575 and 0.564, respectively. If in a particular game each of these players get an "and one" and goes to the line one time, what is the probability that all three players make their foul shots?
4. 70% of disk drives made from Comdrive function properly. If we have a collection of5 disk drives what is the probability that:
a) At least one disk drive doesn't function?
b) At least one disk drive is functioning
5. A coin is tossed five times in succession. Event A is getting a heads outcome three times. While of the following are compatible events to event A? Explain why or why not?
a) Getting a heads on the first coin toss.
b) Getting a tails on the first coin toss.
c) Getting an even number of heads.
6. In a snack size package of M&Ms there are 20 pieces. The pieces come in 6 different colors: red, blue, green, yellow, orange and brown. Assuming that the M&M colors occur with equal probability, what is the probability of getting 5 green M&Ms in a package.
Solve this problem by using
a) The approximation mentioned in Theorem 6
b) The Binomial Distribution and compare answers for a) and b) after you have solved the problem
7. Among Americans aged 65 or older, the prevalence of diabetes is 27%. In Springfield, MI there are 2,000 residents aged 65 and older. What is the probability that there will be between 500 and 600 residents aged 65 and older have diabetes in Springfield, MI? Please choose the appropriate method to approximate this quantity.
8. The probability that I go to the gym on any given day of the week is 30%.
a) Find the probability distribution of the number of times that I go to the gym over the course of one week (7 days).
b) My physician recommends that I go to the gym at least 3 times per week. What is the probability that I follow the physician's recommendation and go to the gym at least 3 times in a one week period?
9. In Los Angeles, CA the probability that it will rain on any given day in the month of June is .02. What is the probability that it will rain once in the month of June in Los Angeles, CA? Please use the appropriate method to approximate this quantity. (Note: you may assume independence).
10. Of the 50 ice cream flavors at J.P. Lick's, 10 of the ice cream flavors have a vanilla base (as opposed to chocolate or some sort of other flavor base). Of the 50 ice cream flavors, 15 ice cream flavors have a candy mix-in. What is the probability that a randomly selected ice cream flavor has a vanilla base and a candy mix in?
11. A company has three different sites: Site 1, Site 2 and Site 3. At Site 1 70% of the employees are UConn alum, at Site 2 20% of the employees are UConn alum, at Site 3 10% are UConn alum. There are an equal number of employees at each of the three sites. If an employee is randomly selected for Employee of the Month what is the probability that they are a UConn alum?