In a class of 30 students, 4 of them have caught the flu. If a teacher randomly selects 2 students, what is the probability that both of them do not have the flu?

Question

In a class of 30 students, 4 of them have caught the flu. If a teacher randomly

selects 2 students, what is the probability that both of them do not have the flu?

Answer 1

Probability is (desired outcome)/(total sample space). So if there are 8 balls, 1 red and 7 white, and you want one red ball, then the probability will be 1/8. In this case, your desired outcome is the number of combinations of 2 people who don't have the flu, so C(26, 2). The sample space is every combination of 2 people, no matter if they are sick or not: C(30, 2). Thus, the probability is C(26, 2)/C(30, 2) = ((26*25)/(2*1))/((30*29)/(2*1)) = (26/30)(25/30).

You could also do it by thinking, the probability of getting one person who is not sick is 26/30, and the probability of getting another person who is not sick is 25/29, so the probability of getting 2 people who aren't sick is (26/30)(25/29), which is what I think Mark did, but I think the first method is more generalizable.

If you're confused about how to do combinations and stuff (I know I was), I would recommend watching Eddie Woo's Youtube videos about the topic. Unfortunately, I can't explain all of that here; there's way too much.

Answer 2

(26/30)(25/29) = ?