Question

Suppose that 8% of the students in your school are Swedish. If you stop students at random in the hall way and ask whether they're Swedish what is the probability that the first Swedish person you find is on your third try? Enter your answer as a decimal rounded to three decimal places, not as a percent.

Answer 1

To find the probability of finding the first Swedish person on the third try, consider the probability of not finding a Swedish person on the first two tries and then finding one on the third try.

Step-by-step explanation:

To find the probability that the first Swedish person you find is on your third try, you need to consider the probabilities of not finding a Swedish person on the first two tries and then finding one on the third try.

Since 8% of the students are Swedish, the probability of not finding a Swedish person on one try is 92% or 0.92. Therefore, the probability of not finding a Swedish person on the first two tries is 0.92 x 0.92 = 0.8464.

Now, since you stop students at random, the probability of finding a Swedish person on the third try is the complement of not finding a Swedish person on the first two tries, which is 1 - 0.8464 = 0.1536.

Answer 2

Given that 8% of the students are Swedish, this means that 100 - 8 = 92% are not Swedish.

Let S represent the event that a student is Swedish and N represent the event that a student is not a Swedish.

Then, the probability that a student chosen at random is a Swedish, P(S), = 8% = 0.08
The probability that a student chosen at random is not a Swedish, P(N), = 92% = 0.92

That the first Swedish person found was on the third trial means that the first and second trial produced a non-Swedish.

Therefore, the required probability = 0.92 x 0.92 x 0.08 = 0.068 to three decimal places.