hey... first time user and really lost. wondering if someone can help:

Based on data from the Statistical Abstract of the United States, 112th Edition, only about 14%
of senior citizens (65 years old or older) get the flu each year. However, about 24% of the
people under 65 years old get the flu each year. In the general population, there are 12.5% senior
citizens (65 years old or older).
a) What is the probability that a person selected at random from the general population is a
senior citizen who will get the flu this year?
b) What is the probability that a person selected at random from the general population is a
person under age 65 who will get the flu this year?
c) Answer parts a) and b) for a community that has 50% senior citizens?

where did the o.875 come from

a)(0.125) x (0.14) = ?

b)(0.875) x (0.24) =
c)(0.50)x(0.14) + (0.50)x(0.24) = ?

yea where did the 0.875 come from

0.875 is the percent of the population that are under 65

Sure, I can help you with that.

To solve these probability problems, we need to use some basic concepts of probability and percentages. Let's break down each part of the question.

a) What is the probability that a person selected at random from the general population is a senior citizen who will get the flu this year?

To find this probability, we need to multiply two percentages together: the percentage of senior citizens in the general population and the percentage of senior citizens who get the flu.

1. Start by converting the percentage of senior citizens in the general population from a percentage to a decimal. In this case, it is 12.5%, which is equivalent to 0.125 (divide by 100).

2. Next, convert the percentage of senior citizens who get the flu from a percentage to a decimal. This is 14%, which is equivalent to 0.14 (divide by 100).

3. Multiply these two decimals together: 0.125 * 0.14 = 0.0175.

So, the probability that a person selected at random from the general population is a senior citizen who will get the flu this year is 0.0175, or 1.75%.

b) What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year?

Again, we need to multiply two percentages together: the percentage of people under age 65 in the general population and the percentage of people under age 65 who get the flu.

1. Start by converting the percentage of people under age 65 in the general population from a percentage to a decimal. In this case, it is 100% - 12.5% (senior citizens) = 87.5%. This is equivalent to 0.875.

2. Convert the percentage of people under age 65 who get the flu from a percentage to a decimal. This is 24%, which is equivalent to 0.24.

3. Multiply these two decimals together: 0.875 * 0.24 = 0.21.

So, the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year is 0.21, or 21%.

c) Answer parts a) and b) for a community that has 50% senior citizens?

Since the community has 50% senior citizens, the percentage of people under age 65 would be 100% - 50% = 50%.

Using the same formulas as before, you can calculate the probabilities as follows:

a) Probability of a senior citizen getting the flu = 50% (0.50) * 14% (0.14) = 0.07 (7%).

b) Probability of a person under age 65 getting the flu = 50% (0.50) * 24% (0.24) = 0.12 (12%).

So, in a community with 50% senior citizens, the probability of a senior citizen getting the flu is 7% and the probability of a person under age 65 getting the flu is 12%.