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Section 3.1 #35: A company is conducting a survey to determine how prepared people are for a long-term power outage, natrual disaster, or terrorist attack. The frequency distribution below shows the results. What is the probability that the next person surveyed is "very prepared"?
 Response Number of times, $f$ Very prepared 259 Somewhat prepared 952 Not too prepared 552 Not at all prepared 336 Not sure 63

Solution: The total number of responses is $$259+952+552+337+63=2163.$$ Therefore the probability of "very prepared" is $$P(\mathrm{very \hspace{2pt} prepared})=\dfrac{259}{2163}=0.1197.$$ Section 3.1 #40: Use the frequency distribution below, which shows the number of American voters (in millions) according to age. Find the probability that a voter chosen at random is 45 to 64 years old.
 Ages of voters Frequency, $f$ (in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3

Solution: The sum of the frequencies is $$4.2+7.9+20.5+22.9+53.5+28.3=137.3.$$ Therefore the probability a voter is 45 to 64 years old is $$\dfrac{53.5}{137.3}=0.3896...$$ Section 3.1, #42: Classify as classical probability, empirical probability, or subjective probability: the probability of choosing 6 numbers from 1 to 40 that match the 6 numbers drawn by a state lottery is $\dfrac{1}{3,838,380} \approx 0.00000026.$
Solution: Classical probability -- this problem can be analyzed entirely mathematically without looking at collected data.

Section 3.1, #47: The age distribution of the residents of San Ysidro, New Mexico, is shown below. Find the probability of Event A: "randomly choosing a resident who is not 15 to 29 years old".
 Ages Frequency, $f$ 0-14 38 15-29 20 30-44 31 45-59 53 60-74 36 75 and over 15

Solution: First sum the frequencies:
$$38+20+31+53+36+15=193.$$ Now the requested probability is $$\dfrac{38+31+53+36+15}{193} = \dfrac{173}{193}=0.8963.$$

Section 3.1, #51: A probability experiment consists of rolling a six-sided die and spinning a spinner with a $\dfrac{1}{4}$ chance of landing on one of the colors yellow, red, blue, and green. Use a tree diagram to find the probability of the event A: "rolling a 5 and the spinner landing on blue".
Solution: First draw the tree diagram: From this we see there are a total of 24 possible outcomes (count the lines at the bottom). There is exactly one way to roll a 5 and land on blue, so the probability being requested is $$\dfrac{1}{24}=0.04166.$$