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Chapter 3: Q95SE (page 203)
A sample space consists of three sample points,, with, and.
Therefore, the results are
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Which events are independent?Use your intuitive understanding of independence to form an opinion about whether each of the following scenarios represents independent events.
a.The results of consecutive tosses of a coin.
b.The opinions of randomly selected individuals in a pre-election poll.
c.A Major League Baseball player's results in two consecutive at-bats.
d.The amount of gain or loss associated with investments in different stocks if these stocks are bought on the same day and sold on the same day 1 month later.
e.The amount of gain or loss associated with investments in different stocks bought and sold in different time periods, 5 years apart.
f.The prices bid by two different development firms in response to a building construction proposal.
Ranking razor blades.The corporations in the highly competitive razor blade industry do a tremendous amount of advertising each year. Corporation G gave a supply of three top-name brands, G, S, and W, to a consumer and asked her to use them and rank them in order of preference.
The corporation was, of course, hoping the consumer would prefer its brand and rank it first, thereby giving them some material for a consumer interview advertising campaign. If the consumer did not prefer one blade over any other but was still required to rank the blades, what is the probability that
a.The consumer ranked brand G first?
b.The consumer ranked brand G last?
c.The consumer ranked brand G last and brand W second?
d.The consumer ranked brand W first, brand G second, and brand S third?
Speeding linked to fatal car crashes. According to the National Highway Traffic and Safety Administration鈥檚 National Center for Statistics and Analysis (NCSA), 鈥淪peeding is one of the most prevalent factors contributing to fatal traffic crashes鈥� (NHTSA Technical Report, August 2005). The probability that speeding is a cause of a fatal crash is .3. Furthermore, the probability that speeding and missing a curve are causes of a fatal crash is .12. Given speeding is a cause of a fatal crash, what is the probability that the crash occurred on a curve?
Two fair dice are tossed, and the face on each die is observed.
showing on each die}
Sum of two numbers showing is}
Sum of two numbers showing is even}
Are you really being served red snapper? Red snapper is arare and expensive reef fish served at upscale restaurants. Federal law prohibits restaurants from serving a cheaper, look-alike variety of fish (e.g., vermillion snapper or lane snapper) to customers who order red snapper. Researchers
at the University of North Carolina used DNA analysis to examine fish specimens labeled 鈥渞ed snapper鈥� that were purchased from vendors across the country (Nature, July 15, 2004). The DNA tests revealed that 77% of the specimens were not red snapper but the cheaper, look-alike variety of fish.
a. Assuming the results of the DNA analysis are valid, what is the probability that you are actually served red snapper the next time you order it at a restaurant?
b. If there are five customers at a chain restaurant, all who have ordered red snapper, what is the probability that at least one customer is actually served red snapper?
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