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

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.