Econ 310, Spring 2014- Week 3:
Problem 1- You go to Vegas to play craps; luckily, Econ 310 has prepared you to solve the following problems:
1. Are rolls of two dice dependent or independent events?
2. With one die, what's the P(rolling a six)? What's the probability of not rolling a six?
3. What's the probability of rolling an even number on one die?
4. You know that you rolled an even number; given that, what's the probability that the number you rolled is a 2?
5. What's the probability of rolling two sixes, using two dice simultaneously? What is the probability of rolling no sixes between both dice? Try drawing a probability tree.
6. What is the probability of rolling an even number on one of the two dice? On both dice?
7. P(sum of two dice equals seven)?
8. Suppose you roll a die 5 times. What's the probability that you roll a 2 all 5 times?
Problem 2- The 4 aces are removed from a deck of cards. A coin is tossed and one of the aces is chosen. What is the probability of getting heads on the coin and the ace of hearts? Draw a tree diagram to illustrate the sample space.
Problem 3- Consider the following joint probability table:
|
|
A
|
AC
|
|
B
|
.15
|
.25
|
|
BC
|
.40
|
.20
|
1. What is P(A and B)? What is P(AC and BC)? What is P(A)? What is P(BC)?
2. What is P(A|B)? What is P(B|A)? What is P(A or B)?
3. Are A and B independent?
Problem 4- Suppose that exactly half of the population are males .5% of males and only 0.25% of females are color blind. A person is chosen at random and that person is color blind. What's the probability that the person is a male?
Problem 5- Suppose you have a diagnostic test for a rare disease that affects 0.1% of the population of Americans (300 million adults). Your test is pretty good at determining if you have the disease, conditional on actually having the disease-in fact, 95% of people with the disease will test positive. However, your test also has some false positives-in fact, 10% of people who do not have the disease will also test positive. Would you recommend this test? Why or why not?
Problem 6- Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time. When it doesn't rain, he incorrectly forecasts rain 20% of the time. What is the probability that it will rain on the day of Marie's wedding?
Problem 7- Suppose that we have 3 cards identical in form except that both sides of the first card are colored red, both sides of the second card are color black, and one side of the third card is colored red and the other side black. The 3 cards are mixed up in a hat, and 1 card is randomly selected and put down on the ground. If the upper side of the chosen card is colored red, what is the probability that the other side is colored black?