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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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Confidence of feedback information for improving quality. In the semiconductor manufacturing industry, a key to improved quality is having confidence in the feedback generated by production equipment. A study of the confidence level of feedback information was published in Engineering Applications of Artificial Intelligence(Vol. 26, 2013). At any point in time during the production process, a report can be generated. The report is classified as either 鈥淥K鈥� or 鈥渘ot OK.鈥� Let Arepresent the event that an 鈥淥K鈥� report is generated in any time period (t).Let Brepresent the event that an 鈥淥K鈥� report is generated in the next time period. Consider the following probabilities:
,, and.
a. Express the event B|Ain the words of the problem.
b. Express the event B|in the words of the problem.
c. Find.
d. Find.
e. Find.
f. Use the probabilities, parts d and e, to find P(B).
g. Use Bayes鈥� Rule to find P(A|B), i.e., the probability that an 鈥淥K鈥� report was generated in one time period(t), given that an 鈥淥K鈥� report is generated in the next time period.
Most likely coin-tossing sequence. In Parade Magazine鈥檚 (November 26, 2000) column 鈥淎sk Marilyn,鈥� the following question was posed: 鈥淚 have just tossed a [balanced] coin 10 times, and I ask you to guess which of the following three sequences was the result. One (and only one) of the sequences is genuine.鈥�
(1) H HHHHHHHHH
(2) H H T T H T T H HH
(3) T TTTTTTTTT
A pair of fair dice is tossed. Define the following events:
A: [Exactly one of the dice shows a 1.]
B: [The sum of the numbers on the two dice is even.]
a. Identify the sample points in the events
b. Find the probabilities of all the events from part a by summing the probabilities of the appropriate sample points.
C. Using your result from part b, explain why A and B are not mutually exclusive.
d. Find using the additive rule. Is your answer the same as in part b?
Patient medical instruction sheets. Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing patients鈥� awareness of the problem is for physicians to provide patient medication instruction (PMI) sheets. The American Medical Association, however, has found that only 20% of the doctors who prescribe drugs frequently distribute PMI sheets to their patients. Assume that 20% of all patients receive the PMI sheet with their prescriptions and that 12% receive the PMI sheet and are hospitalized because of a drug-related problem. What is the probability that a person will be hospitalized for a drug-related problem given that the person received the PMI sheet?
Cell phone handoff behaviour. A 鈥渉andoff鈥� 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?
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