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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"?
ResponseNumber of times, $f$
Very prepared259
Somewhat prepared952
Not too prepared552
Not at all prepared336
Not sure63

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 votersFrequency, $f$ (in millions)
18 to 204.2
21 to 247.9
25 to 3420.5
35 to 4422.9
45 to 6453.5
65 and over28.3

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".
AgesFrequency, $f$
0-1438
15-2920
30-4431
45-5953
60-7436
75 and over15

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 $$\dfrac{1}{24}=0.04166.$$