Final answer:
To find the probability that a student plays both the flute and piano, we subtract the number of students who play only the flute or only the piano plus the number of students who play neither instrument from the total number of students. Then, we divide the number of students who play both instruments by the total number of students to get the probability.
Step-by-step explanation:
To find the probability that a student plays both the flute and piano, we need to determine how many students play both instruments. From the given information, we know that 2 students play the flute only, 11 students play the piano only, and 1 student plays neither instrument. Since the total number of students is 17, we can subtract the number of students who play only the flute or only the piano plus the number of students who play neither instrument from 17 to find the number of students who play both instruments: 17 - 2 - 11 - 1 = 3.
Therefore, there are 3 students who play both the flute and piano. The probability of selecting a student who plays both instruments at random is equal to the number of students who play both instruments divided by the total number of students: 3 / 17 = 0.1765 or 17.65% (rounded to two decimal places).