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

Assume that the event of a student being Swedish is S and that the event of the student not being Swedish is nS.

We are given that 8% of the students are Swedish. This would mean that
100-8 = 92% of the students are not Swedish.

Now, we will get the probability for each event:
probability of a student being Swedish = P(S) = 8% = 0.08
probability of a student not being Swedish = P(nS) = 92% = 0.92

We are given that the first Swedish person is found at the third trial, this means that the first and second trials were not Swedish.
We can get the probability as follows:
Probability of Swedish at third trial = 0.92 * 0.92 * 0.08 = 0.067712
Rounding the answer to three decimal places would give us:
probability of Swedish at third trial = 0.068