Based on data from a statistical abstract only about 12 of...

Based on data from a statistical abstract, only about 12% of senior citizens (65 years old or older) get the flu each year. However, about 25% of the people under 65 years old get the flu each year. In the general population, there are 13.5% senior citizens (65 years old or older). (Round your answers to three decimal places.) (a) What is the probability that a person selected at random from the general population is senior citizen who will get the flu this season? (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) Repeat parts (a) and (b) for a community that has 93% senior citizens. (a) (b) (d) Repeat parts (a) and (b) for a community that has 55% senior citizens. (a) (b)

Transcript

00:01 In this question we're given in a general population, 13 .5 % are senior citizens, or whom 12 % get flu each year, and 25 % of people under 65 years old get the flu each year.

00:15 Now, a person is randomly selected from the general population.

00:19 I'm going to let s denote the event a person is a senior citizen, and f denote the event, a person who gets flu this season.

00:27 So in these three diagram, s here refers to a person who is a senior citizen.

00:32 S prime will be the complement of s and that will be the person is not a senior citizen.

00:38 Now f will be a person who get flu, f prime will be a person will not get flu.

00:44 So over here is the probability of s and that will be probability a person is a senior citizen that is 13 .5 % or 0 .135 decimal.

00:56 We know that this part of the 3 will add out the probability of 1.

01:00 So to get probability of s prime will take 1 minus 0 .135 and that will be 0 .865.

01:09 Over here is 12 % of senior citizens that flu is here.

01:15 So this is actually the conditional probability of a person getting flu given he is senior citizen.

01:22 So it's probability of f given as has already occurred.

01:26 And so this will be 12 % or 0 .12.

01:32 Over here is 25 % of people under 65 years old, having flu and this will be the conditional probability of event f given s prime and that will be 25 % or 0 .25.

01:50 In part a we want to find the probability a person is a senior citizen so event s who will get flu this season so it's a senior citizen and will get flu now n in probability is intersect or is union so n will be intersected and get flu is even f.

02:11 So we want to find probability of s intercept f.

02:14 By formula is probability of s times probability of f given s.

02:20 So this is actually simply taking 0 .135 times 0 .12.

02:34 So that would be 0 .0163 decimal place...

Question

Please give Ace some feedback