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Chapter 3: Q97E (page 203)
Consider two events A and B, with,,and
a.Are A and B mutually exclusive?
b.Are A and B independent?
a. The events are mutually exclusive.
b. The events are not independent.
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Working mothers with children. The U.S. Census Bureaureports a growth in the percentage of mothers in the workforce who have infant children. The following table gives a breakdown of the marital status and working status of mothers with infant children in the year 2014. (The numbers in the table are reported in thousands.) Consider the following events: A = {Mom with infant works}, B = {Mom with infant is married}. Are A and B independent events?
working | Not working | |
Married | 6027 | 4064 |
No spouse | 2147 | 1313 |
(Data from U.S. Census Bureau, Bureau of LabourStatistics, 2014 (Table 4).
An experiment results in one of three mutually exclusive events, A, B, or C. It is known that P (A)= .30, P(B)= .55 , and P(C)= .15. Find each of the following probabilities:
a.
b.
c. P (A/B)
d.
e. Are B and C independent events? Explain.
Blood diamonds.According to Global Research News(March 4, 2014), one-fourth of all rough diamonds producedin the world are blood diamonds. (Any diamond that is mined in a war zone—often by children—to finance a warlord’s activity, an insurgency, or an invading army’s effort is considered a blood diamond.) Also, 90% of the world’s rough diamonds are processed in Surat, India, and, of these diamonds one-third are blood diamonds.
a.Find the probability that a rough diamond is not a blood diamond.
b.Find the probability that a rough diamond is processed in Surat and is a blood diamond.
Reliability of gas station air gauges. Tire and automobile manufacturers and consumer safety experts all recommend that drivers maintain proper tire pressure in their cars. Consequently, many gas stations now provide air pumps and air gauges for their customers. In a Research Note(Nov. 2001), the National Highway Traffic Safety Administration studied the reliability of gas station air gauges. The next table gives the percentage of gas stations that provide air gauges that over-report the pressure level in the tire.
a. If the gas station air pressure gauge reads 35 psi, what is the probability that the pressure is over-reported by 6 psi or more?
b. If the gas station air pressure gauge reads 55 psi, what is the probability that the pressure is over-reported by 8 psi or more?
c. If the gas station air pressure gauge reads 25 psi, what is the probability that the pressure is not over-reported by 4 psi or more?
d. Are the events A= {over report by 4 psi or more} and B= {over report by 6 psi or more} mutually exclusive?
e.Based on your answer to part d, why do the probabilities in the table not sum to 1?
Ambulance response time.Geographical Analysis(Jan. 2010) presented a study of emergency medical service (EMS) ability to meet the demand for an ambulance. In one example, the researchers presented the following scenario. An ambulance station has one vehicle and two demand locations, A and B. The probability that the ambulance can travel to a location in under 8 minutes is .58 for location A and .42 for location B. The probability that the ambulance is busy at any point in time is .3.
a.Find the probability that EMS can meet the demand for an ambulance at location A.
b.Find the probability that EMS can meet the demand for an ambulance at location B.
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