Question

finding the probability of the complement of an event the age distribution of the residents of ithaca, new york, is shown at the left. in exercises 59–62, find the probability of the event. (source: u.s census bureau) 59. event a: a randomly chosen resident of ithaca is not 18 to 24 years old. 60. event b: a randomly chosen resident of ithaca is not 25 to 39 years old. 61. event c: a randomly chosen resident of ithaca is not less than 18 years old. 62. event d: a randomly chosen resident of ithaca is not 70 years old or older. table for exercises 59–62 (with the table: ages (0–17, 18–24, 25–39, 40–54, 55–69, 70 and over) and frequency, f (2416, 16598, 5293, 2726, 2140, 1396))

Explanation:

Step1: Calculate total residents

Sum all frequencies: $2416 + 16598 + 5293 + 2726 + 2140 + 1396 = 30569$

Step2: Find P(not 18-24) for 59

$1 - \frac{16598}{30569} = \frac{30569 - 16598}{30569} = \frac{13971}{30569} \approx 0.457$

Step3: Find P(not 25-39) for 60

$1 - \frac{5293}{30569} = \frac{30569 - 5293}{30569} = \frac{25276}{30569} \approx 0.827$

Step4: Find P(not <18) for 61

$1 - \frac{2416}{30569} = \frac{30569 - 2416}{30569} = \frac{28153}{30569} \approx 0.921$

Step5: Find P(not ≥70) for 62

$1 - \frac{1396}{30569} = \frac{30569 - 1396}{30569} = \frac{29173}{30569} \approx 0.954$

Answer:

1. $\frac{13971}{30569} \approx 0.46$
2. $\frac{25276}{30569} \approx 0.83$
3. $\frac{28153}{30569} \approx 0.92$
4. $\frac{29173}{30569} \approx 0.95$