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Chapter 5: Q 74. (page 330)
Teachers and college degrees Select an adult at random. Define events : a person has earned a college degree, and : person’s career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.
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During World War II, the British found that the probability that a bomber is lost through enemy action on a mission over occupied Europe was Assuming that missions are independent, find the probability that a bomber returned safely from missions.
Texas hold ’em In popular Texas hold ’em variety of poker, players make their best five-card poker hand by combining the two cards they are dealt with
three of five cards available to all players. You read in a book on poker that if you hold a pair (two cards of the same rank) in your hand, the probability of getting four of a kind is
(a) Explain what this probability means.
(b) Why doesn’t this probability say that if you play
1000 such hands, exactly will be four of a kind?
An unenlightened gambler
(a) A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes five consecutive reds occur and bets
heavily on black at the next spin. Asked why he explains that black is “due by the law of averages.” Explain to the gambler what is wrong with this reasoning.
(b) After hearing you explain why red and black are still equally likely after five reds on the roulette wheel, the gambler moves to a poker game. He is dealt five straight red cards. He remembers what you said and assumes that the next card dealt in the same hand is equally likely to be red or black. Is the gambler right or wrong, and why?
Spinning a quarter With your forefinger, hold a new quarter (with a state featured on the reverse) upright, on its edge, on a hard surface. Then flick it with your other forefinger so that it spins for some time before it falls and comes to rest. Spin the coin a total of 25 times, and record the results.
(a) What’s your estimate for the probability of heads? Why?
(b) Explain how you could get an even better estimate.
Treating low bone density (4.2) Fractures of the spine are common and serious among women with advanced osteoporosis (low mineral density in the
bones). Can taking strontium ranelate help? A large medical trial assigned 1649 women to take either strontium ranelate or a placebo each day. All of
the subjects had osteoporosis and had had at least one fracture. All were taking calcium supplements and receiving standard medical care. The response variables were measurements of bone density and counts of new fractures over three years. The subjects were treated at medical centers in different countries. Outline an appropriate design for this experiment. Explain why this is the proper design.
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