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Chapter 5: Q 8. (page 294)
Keep on tossing The figure below shows the results of two different sets of coin tosses. Explain what this graph says about chance behavior in the short run and the long run.
The probability of getting ahead is around a third of the time
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Probability models? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.
(a) Roll a die and record the count of spots on the up-face: P(1) = 0, P(2) = 1/6, P(3) = 1/3, P(4) = 1/3,
P(5) = 1/6, P(6) = 0.
(b) Choose a college student at random and record gender and enrollment status: P(female full-time) = 0.56, P(male full-time) = 0.44, P(female part-time) = 0.24, P(male part-time) = 0.17.
(c) Deal a card from a shuffled deck: P(clubs) = 12/52, P(diamonds) = 12/52, P(hearts) = 12/52,
P(spades) = 16/52.
Tossing coins Imagine tossing a fair coin times. (a) What is the sample space for this chance
process? (b) What is the assignment of probabilities to outcomes in this sample space?
Box of chocolates According to Forrest Gump, 鈥淟ife is like a box of chocolates. You never know what you鈥檙e gonna get.鈥� Suppose a candy maker offers a
special 鈥淕ump box鈥� with chocolate candies that look the same. In fact, of the candies have soft centers and 6 have hard centers. Choose of the
candies from a Gump box at random.
(a) Draw a tree diagram that shows the sample space of this chance process.
(b) Find the probability that one of the chocolates has a soft center and the other one doesn鈥檛.
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.
Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water off. How many
students in the sample would need to say 鈥淣o鈥� to provide convincing evidence that fewer than half of the students at the school brush with the water off? The Fathom dot plot below shows the results of taking 200 SRSs of 60 students from a population in which the true proportion who brush with the
water off is 0.50.
(a) Suppose 27 students in the class鈥檚 sample say 鈥淣o.鈥� Explain why this result does not give convincing evidence that fewer than half of the school鈥檚 students brush their teeth with the water off.
(b) Suppose 18 students in the class鈥檚 sample say 鈥淣o.鈥� Explain why this result gives strong evidence that fewer than 50% of the school鈥檚 students brush
their teeth with the water off.
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