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Chapter 5: Q 2.2. (page 317)
Shuffle a standard deck of cards, and turn over the top two cards, one at a time. Define events : first card is a heart, and : second card is a heart.
No, events are independent.
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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.
The birthday problem What’s the probability that in a randomly selected group of unrelated people, at least two have the same birthday? Let’s make two
assumptions to simplify the problem. First, we’ll ignore the possibility of a February birthday. Second, we assume that a randomly chosen person is equally likely to be born on each of the remaining days of the year.
(a) How would you use random digits to imitate one repetition of the process? What variable would you measure?
(b) Use technology to perform repetitions. Record the outcome of each repetition.
(c) Would you be surprised to learn that the theoretical probability is ? Why or why not?
Who eats breakfast? Refer to Exercise 49.
(a) Construct a Venn diagram that models the chance process using events B: eats breakfast regularly, and M: is male.
(b) Find Interpret this value in context.
(c) Find Interpret this value in context.
Crawl before you walk (3.2) At what age do babies learn to crawl? Does it take longer to learn in the winter, when babies are often bundled in clothes that
restrict their movement? Perhaps there might even be an association between babies’ crawling age and the average temperature during the month they first try to crawl (around six months after birth). Data were collected from parents who brought their babies to the University of Denver Infant Study Center to participate in one of a number of studies. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of four feet within one minute. Information was obtained on infants ( boys and girls). Crawling age is given in weeks, and average temperature (in °F) is given for the month that is six months after the birth month. Analyze the relationship between average crawling age and average temperature. What do you conclude about when babies learn to crawl?
Roulette, An American roulette wheel hasslots with numbers through as shown in the figure. Of the numbered slots, are red, are black, and —the and —are green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced, the ball
is equally likely to settle in any of the numbered slots. Imagine spinning a fair wheel once. Define events B: ball lands in a black slot, and E: ball lands in an even numbered slot. (Treat and as even numbers.)
(a) Make a two-way table that displays the sample space in terms of events B and E.
(b) Find P(B) and P(E).
(c) Describe the event “B and E” in words. Then find P(B and E). Show your work.
(d) Explain why P(B or E) ≠ P(B) + P(E). Then use the general addition rule to compute P(B or E).
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