Finding the Probability of the Complement of an Event The age ...

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)
61. Event C: A randomly chosen resident of Ithaca is not less than 18 years old.

61. Event C: A randomly chosen resident of Ithaca is not less than 18 years old.

tab2

Accepted Answer

Welcome back, everyone. The table below shows the age distribution of the population of Maple City. What is the probability that a randomly chosen person is not younger than 30 years old? A says about 0.318. B 0.414, C 0.586, and D 0.682. So for this problem, we're going to define an event A. We do not want to choose an individual who is younger than 30 years old. So, we're going to say that A represents an event that an individual is not. Younger Then 30 And we can identify the probability of a using the method of complements. So we're basically subtracting the probability of a not occurring or the complement of a. In other words, the complement of a represents an event that a chosen individual is younger than 30. So when we analyze our table, we can see that there are two age groups corresponding to this scenario, 0 to 14 and 15 to 29. So let's identify the probability of a bar or the complement of a. We have to recall that we basically take the number of favorable outcomes. So we have to add those aged between 0 and 14, that's 1,819. And those aged 15 to 29 so were adding 4,257. So this number of favorable outcomes is going to be divided by the total number of outcomes. And those will be all of the individuals given to us in the table. So what we have to do is simply sum the numbers in the second column. We begin with 1,819, followed by 4,257, 3,926, 2,744. And finally, 1,929, that would be our denominator. And then we can simply rewrite our numerator and the denominator. In the numerator we have 6000. 76 and in our denominator we have 14,000. 675 And then we can solve for the probability of a. Which is 1 minus 6000. 76 divided by 1 divided by 14,675 subtracting, we get 0.586 rounded to three decimal places, which is about 0.586 and it corresponds to the answer choice C. Thank you for watching.

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