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Chapter 4: Q2 (page 143)
Probability Rewrite the following statement so that the likelihood of rain is expressed as a value between 0 and 1: 鈥淭he probability of rain today is 25%.鈥�
The probability of rain (between 0 and 1) is 0.25.
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Interpreting Weather While this exercise was being created, Weather.com indicated that there was a 60% chance of rain for the author鈥檚 home region. Based on that report, which of the following is the most reasonable interpretation?
a. 60% of the author鈥檚 region will get rain today.
b. In the author鈥檚 region, it will rain for 60% of the day.
c. There is a 0.60 probability that it will rain somewhere in the author鈥檚 region at some point during the day.
Confusion of the Inverse Using the same events F and H described in Exercise 3, describe confusion of the inverse.
Probability from a Sample Space. In Exercises 33鈥�36, use the given sample space or construct the required sample space to find the indicated probability.
Three Children Using the same sample space and assumption from Exercise 33, find the probability that when a couple has three children, there are exactly two girls.
Odds. In Exercises 41鈥�44, answer the given questions that involve odds.
Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number.
a. What is your probability of winning?
b. What are the actual odds against winning?
c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet \(18 and win?
d. How much profit would you make on the \)18 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? (Recommendation: Don鈥檛 actually try to convince any casino of this; their sense of humor is remarkably absent when it comes to things of this sort.)
In Exercises 29 and 30, find the probabilities and indicate when the 鈥�5% guideline for cumbersome calculations鈥� is used.
Medical Helicopters In the same study cited in the preceding exercise, among the 47,637 patients transported by helicopter, 188 of them left the treatment center against medical advice, and the other 47,449 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left the treatment center against medical advice?
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