Chapter 5: Q R5.1. (page 334)
Rainy days The TV weatherman says, “There’s a 30% chance of rain tomorrow.” Explain what this statement means.
It will rain tomorrow.
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You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about This means that (a) in every bridge deals, each player has one ace exactly times.
(b) in one million bridge deals, the number of deals on which each player has one ace will be exactly
(c) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to
(d) in a very large number of bridge deals, the average number of aces in a hand will be very close to
(e) None of these
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.
Going pro Only of male high school basketball, baseball, and football players go on to play at the college level. Of these, only enter major league professional sports. About of the athletes who compete in college and then reach the pros have a career of more than years. What is the probability that a high school athlete who plays basketball, baseball, or football competes in college and then goes on to have a pro career of more than years? Show your work.
Stoplight On her drive to work every day, Ilana passes through an intersection with a traffic light. The light has a probability of 1/3 of being green when she gets to the intersection. Explain how you would use each chance device to simulate whether the light is red or green on a given day.
(a) A six-sided die
(b) Table D of random digits
(c) A standard deck of playing cards
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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