1.) Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic (debit and credit) cards in making purchases (Associated Press, January 16, 2006). The results of the study provided the following probabilities.
The probability that a consumer uses a plastic card when making a purchase is .37.
Given that the consumer uses a plastic card, there is a .19 probability that the consumer is 18 to 24 years old.
Given that the consumer uses a plastic card, there is a .81 probability that the consumer is more than 24 years old.
U.S. Census Bureau data show that 14% of the consumer population is 18 to 24 years old.
a.)Given the consumer is 18 to 24 years old, what is the probability that the consumer uses a plastic card (to 4 decimals)?
b.)Given the consumer is over 24 years old, what is the probability that the consumer uses a plastic card (to 4 decimals)?
2.) The prior probabilities for events A1 and A2 are P(A1) = .40 and P(A2) = .60. It is also known that P(A1 (intersects the upside down U) A2) = 0. Suppose P(B | A1) = .20 and P(B | A2) = .05.
a.)Compute P(B).
3.)Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars accounted for 18% of the vehicles on the road, but accidents involving small cars led to 11,898 fatalities during a recent year (Reader's Digest, May 2000). Assume the probability a small car is involved in an accident is .18. The probability of a fatality in an accident involving a small car is .128 and the probability of a fatality in an accident involving a bigger car is .05. Suppose you learn about an accident involving a fatality.
a.) What is the probability a small car was involved in the accident (to 2 decimals)?
4.)In an article about investment growth, Money magazine reported that drug stocks show powerful long-term trends and offer investors unparalleled potential for strong and steady gains. The federal Health Care Financing Administration supports this conclusion through its forecast that annual prescription drug expenditures will reach $ 366 billion by 2010, up from $ 117 billion in 2000. Many individuals age 65 and older rely heavily on prescription drugs. For this group, 82% take prescription drugs regularly, 55% take three or more prescriptions regularly, and 40% currently use five or more prescriptions. In contrast, 49% of people under age 65 take prescriptions regularly, with 37% taking three or more prescriptions regularly and 28% using five or more prescriptions (Money, September 2001). The U.S. Census Bureau reports that of the 281,421,906 people in the United States, 34,991,753 are age 65 years and older (U.S. Census Bureau, Census 2000).
a.)Given a person uses five or more prescriptions, compute the probability that the person is age 65 or older (to 2 decimals).
5.)A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of 7.5 cases involving negligence, and payments were made in one out of every two claims.
a.)What is the probability a person admitted to the hospital will die from a treatment caused injury (to 3 decimals)?
6.)An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P(high-quality oil)= .50
P(medium-quality oil)= .20
P(No oil)= .30
a.) After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test follow.
P(soil | high-quality oil) =.20
P(soil | medium-quality oil) =.80
P(soil | no oil) =.20
Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 2 decimals).
P(high-quality oil | soil) =
P(medium-quality oil | soil) =
P(no oil | soil) =
b.) What is the new probability of finding oil (to 2 decimals)?
c.) What quality oil is most likely to be found, according to the revised probabilities?
any help on any problem would be greatly appreciated PLEASE and think you even if it's only half of an answer.
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a.)Given the consumer is 18 to 24 years old, what is the probability that the consumer uses a plastic card (to 4 decimals)?
multiply .37 by .19
b.)Given the consumer is over 24 years old, what is the probability that the consumer uses a plastic card (to 4 decimals)?
multiply .37 by .81
Orignal From: Need help really bad Math.?
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