There are 7 people fishing at Lake Connor: 5 have fishing licenses, and 2 do not. An inspector chooses two of the people at random. What is the probability that the first person chosen has a license and the second one does not? Write your answer as a fraction in simplest form.
There are a total of 7 people, so there are a total of 7 possible choices for the first person. There are 5 people with licenses, so the probability that the first person chosen has a license is 5/7. After picking the first person, there are 6 people remaining, so there are a total of 6 possible choices for the second person. There are 2 people without licenses, so the probability that the second person chosen does not have a license is 2/6.
Therefore, the probability that the first person chosen has a license and the second person chosen does not is (5/7) * (2/6) = (5 * 2) / (7 * 6) = 10/42.
To simplify the fraction, we can divide both the numerator and denominator by the greatest common divisor, which is 2. So, the simplified fraction is (10/2) / (42/2) = 5/21.