Final answer:
The probability that each sports team has a female student is 14.51%.
Step-by-step explanation:
In this scenario, there are 15 students and each of them can only join one team. The total number of ways to choose 3 female students from the 15 students is given by the combination formula C(3, 15) = 455.
Next, the number of ways to distribute the 3 female students among the 3 teams such that each team has at least one female student can be calculated. We can choose one team to have 2 female students and the other two teams to have 1 female student each. There are C(1, 3) ways to choose the team with 2 female students. Once this team is chosen, there are C(2, 12) ways to choose 2 female students from the remaining 12 students, and the remaining female student goes to the team that hasn't been chosen yet. Therefore, the number of ways to distribute the female students in this manner is C(1, 3) * C(2, 12) = 66.
The probability that each team has a female student is then calculated as the number of favorable outcomes (66) divided by the total number of possible outcomes (455), which gives a probability of 66/455 = 0.1451 or approximately 14.51%.