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Chapter 3: Q96E (page 203)
For two events A and B, suppose ,,Find.
The value of is 0.8.
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Jai-alai bets. The Quinella bet at the paramutual game of jai-alai consists of picking the jai-alai players that will place first and second in a game irrespective of order. In jai-alai, eight players (numbered 1, 2, 3, . . . , 8) compete in every game.
a. How many different Quinella bets are possible?
b. Suppose you bet the Quinella combination of 2鈥�7. If the players are of equal ability, what is the probability that you win the bet?
Encoding variability in software. At the 2012 Gulf Petrochemicals and Chemicals Association (GPCA) Forum, Oregon State University software engineers presented a paper on modelling and implementing variation in computer software. The researchers employed the compositional choice calculus (CCC)鈥攁 formal language for representing, generating, and organizing variation in tree-structured artefacts. The CCC language was compared to two other coding languages鈥攖he annotative choice calculus (ACC) and the computational feature algebra (CFA). Their research revealed the following: Any type of expression (e.g., plain expressions, dimension declarations, or lambda abstractions) found in either ACC or CFA can be found in CCC; plain expressions exist in both ACC and CFA; dimension declarations exist in ACC, but not CFA; lambda abstractions exist in CFA, but not ACC. Based on this information, draw a Venn diagram illustrating the relationships among the three languages. (Hint: An expression represents a sample point in the Venn diagram.)
Appeals of federal civil trials. The Journal of the American Law and Economics Association (Vol. 3, 2001) publishedthe results of a study of appeals of federal civil trials. Thefollowing table, extracted from the article, gives a breakdownof 2,143 civil cases that were appealed by either theplaintiff or the defendant. The outcome of the appeal, aswell as the type of trial (judge or jury), was determined foreach civil case. Suppose one of the 2,143 cases is selected
at random and both the outcome of the appeal and type of trial are observed.
Jury | Judge | Totals | |
Plaintiff trial win-reserved | 194 | 71 | 265 |
Plaintiff trial win-affirmed/dismissed | 429 | 240 | 669 |
Defendant trial win-reserved | 111 | 68 | 179 |
Defendant trial win- affirmed/dismissed | 731 | 678 | 1030 |
Total | 1465 | 678 | 2143 |
a. Find P (A), where A = {jury trial}.
b. Find P (B), where B = {plaintiff trial win is reversed}.
c. Are A and B mutually exclusive events?
d. Find
e. Find
f. Find
On-the-job arrogance and task performance. Human Performance (Vol. 23, 2010) published the results of a study that found that arrogant workers are more likely to have poor performance ratings. Suppose that 15% of all full-time workers exhibit arrogant behaviors on the job and that 10% of all full-time workers will receive a poor performance rating. Also, assume that 5% of all full-time workers exhibit arrogant behaviors and receive a poor performance rating. Let A be the event that a full-time worker exhibits arrogant behavior. Let B be the event that a full-time worker will receive a poor performance rating.
a. Are the events A and B mutually exclusive? Explain.
b. Find P(B/A).
c. Are the events A and B independent? Explain.
Investing in stocks. From a list of 15 preferred stocks recommended by your broker, you will select three to invest in. How many different ways can you select the three stocks from the 15 recommended stocks?
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