Review Problems for Test 1 PDF

Review problems for Test 1 1. Let A and B be independent events with P (A ∩ B) = 0.2 and P (B|A) = 0.6. a) Are A and B are disjoint? b) Find P (A) and P (B). 2. For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, th...

Review problems for Test 1 1. Let A and B be independent events with P (A ∩ B) = 0.2 and P (B|A) = 0.6. a) Are A and B are disjoint? b) Find P (A) and P (B). 2. For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that the wife will vote on the referendum is 0.28, and the probability that both the husband and the wife will vote is 0.15. a) What is the probability that at least one member of a married couple will vote? b) What is the probability that a wife will vote, given that her husband will vote? c) What is the probability that a husband will vote, given that his wife will not vote? 3. Three cards are drawn in succession, without replacement, from an ordinary deck of playing cards. Find the probability that the event A1 ∩ A2 ∩ A3 occurs, where A1 is the event that the first card is a red ace, A2 is the event that the second card is a 10 or a jack, and A3 is the event that the third card is a king. Do not simplify your answer. 4. Two friends (John and Kevin) who have unpredictable lunch hours agree to meet for lunch at their favorite restaurant whenever possible. Neither wishes to eat at that particular restau- rant alone and each dislikes waiting for the other, so they agree that each will arrive at a random time between 1:00 p.m. and 2:00 p.m. and each will wait for the other either for 10 minutes or until 2:00 p.m. On a given day, what is the probability that the friends will meet? 5. Peter has 8 different books, five of them being the five volumes of The Faerie Queen series by Edmund Spencer. Peter will arrange the books on the bookshelf without looking (i.e. randomly). a) What is the probability that the five volumes of The Faerie Queen series will be next to each other in the proper (increasing) order? b) What is the probability that the five volumes of The Faerie Queen series will be next to each other, but not necessarily in order? c) What is the probability that the five volumes of the series will be in the proper order, but not necessarily next to each other? 6. The following circuit operates if and only if there is a path of functional devices from left to right. The probability that each device functions is as shown. Assume that the probability that a device is functional does not depend on whether or not other devices are functional. What is the probability that the circuit operates?  7. An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. The Altigauge Company makes 80% of the ELTs, the Bryant Company makes 15% of them, and the Chartair Company makes the other 5%. The ELTs made by Altigauge have a 3% rate of defects, the Bryant ELTs have a 6%, and the Chartair ELTs have a 9% rate of defects. If a randomly selected ELT is then tested and is found to be defective, find the probability that it was made by the Altigauge Company. 8. A lot contains 4 good wafers and 3 defective wafers. A quality inspector randomly selects a sample of 3 wafers from this lot. Let X be the number of good wafers in the sample. Find the distribution of X. 1 9. The probability that a patient recovers from a rare blood disease is , and people recover or 3 die from that disease independently of each other. Four people contracted this disease. a) What is the probability that exactly three of them will recover? b) What is the probability that at least two of them will recover? 10. Random variable X has the following distribution: X 0 1 4 1 1 1 P (x) 2 6 3 a) Find the √ variance of X. b) Find E X. c) Find the third moment of X.