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Chapter 3: Q.3-53E (page 193)
For two events, A and B, P(A)= .4, P(B)= .2 , and :
a. Find P (A/B).
b. Find P(B/A).
c. Are A and B independent events?
Answer
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Stock market participation and IQ.Refer to The Journal of Finance(December 2011) study of whether the decisionto invest in the stock market is dependent on IQ, Exercise3.46 (p. 182). The summary table giving the number ofthe 158,044 Finnish citizens in each IQ score/investment category is reproduced below. Again, suppose one of the citizens is selected at random.
IQ Score | Invest in Market | No Investment | Totals |
1 2 3 4 5 6 7 8 9 | 893 1,340 2,009 5,358 8,484 10,270 6,698 5,135 4,464 | 4,659 9,409 9,993 19,682 24,640 21,673 11,260 7,010 5,067 | 5,552 10,749 12,002 25,040 33,124 31,943 17,958 12,145 9,531 |
Totals | 44,651 | 113,393 | 158,044 |
Source:Based on M. Grinblatt, M. Keloharju, and J. Linnainaa, “IQ and Stock Market Participation,” The Journal of Finance, Vol. 66, No. 6, December 2011 (data from Table 1 and Figure 1).
a.Given that the Finnish citizen has an IQ score of 6 or higher, what is the probability that he/she invests in the stock market?
b.Given that the Finnish citizen has an IQ score of 5 or lower, what is the probability that he/she invests in the stock market?
c.Based on the results, parts a and b, does it appear that investing in the stock market is dependent on IQ? Explain.
Cell phone handoff behaviour. A “handoff” is a term used in wireless communications to describe the process of a cell phone moving from the coverage area of one base station to that of another. Each base station has multiple channels (called color codes) that allow it to communicate with the cell phone. The Journal of Engineering, Computing and Architecture (Vol. 3., 2009) published a cell phone handoff behavior study. During a sample driving trip that involved crossing from one base station to another, the different color codes accessed by the cell phone were monitored and recorded. The table below shows the number of times each color code was accessed for two identical driving trips, each using a different cell phone model. (Note: The table is similar to the one published in the article.) Suppose you randomly select one point during the combined driving trips.
| Color code | |||||
0 | 5 | b | c | Total | |
Model 1 | 20 | 35 | 40 | 0 | 85 |
Model 2 | 15 | 50 | 6 | 4 | 75 |
Total | 35 | 85 | 46 | 4 | 160 |
a. What is the probability that the cell phone was using color code 5?
b. What is the probability that the cell phone was using color code 5 or color code 0?
c. What is the probability that the cell phone used was Model 2 and the color code was 0?
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—7. If the players are of equal ability, what is the probability that you win the bet?
Study of why EMS workers leave the job.Refer to the Journal of Allied Health(Fall 2011) study of why emergencymedical service (EMS) workers leave the profession,Exercise 3.45 (p. 182). Recall that in a sample of 244former EMS workers, 127 were fully compensated whileon the job, 45 were partially compensated, and 72 hadnon-compensated volunteer positions. Also, the numbersof EMS workers who left because of retirement were 7 forfully compensated workers, 11 for partially compensatedworkers, and 10 for no compensated volunteers.
a.Given that the former EMS worker was fully compensatedwhile on the job, estimate the probability that theworker left the EMS profession due to retirement.
b.Given that the former EMS worker had a non-compensatedvolunteer position, estimate the probabilitythat the worker left the EMS profession due toretirement.
c.Are the events {a former EMS worker was fully compensatedon the job} and {a former EMS worker left thejob due to retirement} independent? Explain.
Suppose the events are mutually exclusive and complementary events, such that, and . Consider another event A such thatandUse Baye’s Rule to find
a.
b.
c.role="math" localid="1658214716845"
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