1. A department store manager has decided that dress code is necessary for team coherence. Team members are required to wear either blue shirts or red shirts. There are 9 men and 7 women in the team. On a particular day, 5 men wore blue shirts and 4 other wore red shirts, whereas 4 women wore blue shirts and 3 others wore red shirt. Apply the Addition Rule to determine the probability of finding men or blue shirts in the team.
2. Schreibabyism is a rare but real malady inflicting 2% of mathematicians worldwide. Yours truly has recently discovered a screening test for this rare malady, and the finding has just been reported to the International Association of Insane Scientists (IAIS) for publication. Unfortunately, my esteemed colleagues who reviewed my submitted draft discovered that the reliability of this screening test is only 80%. What it means is that it gives a positive result, false positive, in 20% of the mathematicians tested even though they are not afflicted by this horribly-embarrassing malady. What is the probability that one mathematician at random is actually inflicted by this rare disabling malady?
3. We have 7 boys and 3 girls in our church choir. There is an upcoming concert in the local town hall. Unfortunately, we can only have 5 youths in this performance. This performance team of 5 has to by picked randomly from the crew of 7 boys and 3 girls.
a. What is the probability that all 3 girls are picked in this team of 5?
b. What is the probability that none of the girls are picked in this team of 5?
c. What is the probability that 2 of the girls are picked in this team of 5?
4. Texas University believes that only 85% of our registered students will stay registered in a class long enough to purchase the required textbook. Let's pick on our STAT 200 students. According to the Registrar's Office, we have 600 students enrolled in STAT 200 this spring 2014.
Suppose you are the CEO of MBS Direct, and you want to perform a probability analysis. What would be the number of STAT 200 textbook bundles you would order so that you stay below 5% probability of having to back-order from Pearson Custom Publishing?
5. Most of us love Ecuadorian mangoes, but hate buying those that are picked too early. Unfortunately, by waiting until the mangos are almost ripe to pick carries a risk of having 15% of the picked rot upon arrival at the packing facility. If the packing process is all done by machines without human inspection to pick out any rotten mangos, what would be the probability of having at most 2 rotten mangos packed in a box of 12?
Import: Please read carefully....... You are allowed to use technology for the following Problem (Problem #6 and Problem #7), and these two Problems only. Most probably, you have to use technology or you may have to spend hours, if not days, to carry out the necessary calculations by hand. Nonetheless, you should clearly delineate and explain your logic and reasoning on how to tackle this problem.
6. A soda company want to stimulate sales in this economic climate by giving customers a chance to win a small prize for ever bottle of soda they buy. There is a 20% chance that a customer will find a picture of a unicorn at the bottom of the cap upon opening up a bottle of soda. The customer can then redeem that bottle cap with this picture for a small prize. Now, if I buy a 6-pack of soda, what is the probability that I will win something, i.e., at least win a single small prize?
7. Angry Airlines is notorious for its cost-cutting substandard customer service. Consequently, only 85% of the ticket holders will show up for a flight. The Air Lines workhorse, the Boring 878, has 234 seats. UAL, of course, will make extra money by overbooking. However, they have to worry about the FAA fines, and they have to keep a safety margin, say, that there is at least 95% probability that they can accommodate all those who show up for the Boring 878 flight. How many seats can they actually sell in this case?