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Chapter 5: Q 2.3. (page 305)
Explain why . Then use the general addition rule to find.
The likelihood of and the occurrence A or B
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A Titanic disaster Refer to Exercise 64.
(a) Find P(survived | second class).
(b) Find P(survived).
(c) Use your answers to (a) and (b) to determine whether the events “survived” and “second class” are independent. Explain your reasoning.
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?
Sampling senators The two-way table describes the members of the U.S. Senate in a recent year. Suppose we select a senator at random. Consider events D: is a democrat, and F: is female.
(a) Find P(D | F). Explain what this value means.
(b) Find P(F | D). Explain what this value means.
Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.
(a) According to a recent survey, of people aged and older in the United States are addicted to email. To simulate choosing a random sample of
people in this population and seeing how many of them are addicted to email, use a deck of cards. Shuffle the deck well, and then draw one card at a
time. A red card means that person is addicted to email; a black card means he isn’t. Continue until you have drawn cards (without replacement) for the sample.
(b) A tennis player gets of his second serves in play during practice (that is, the ball doesn’t go out of bounds). To simulate the player hitting second serves, look at pairs of digits going across a row in Table D. If the number is between and , the service is in; numbers between and indicate that the service is out.
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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