In a classroom there are 100 students, of whom 40 are boys, 30 wear glasses, and 15 are boys who wear glasses. If one student from the class is randomly selected what is the probability that the student will be a girl who does not wear glasses?
There are 100 students in the class, and we know that 40 of them are boys. Therefore, there must be 100 - 40 = 60 girls in the class.
We also know that 30 students wear glasses, so 100 - 30 = 70 students do not wear glasses.
Out of the 15 boys who wear glasses, we need to find out how many girls wear glasses. Since there are 30 students who wear glasses, and 15 of them are boys, this must mean that 30 - 15 = 15 girls wear glasses.
Now we can find the number of girls who do not wear glasses by taking the total number of girls and subtracting the girls who wear glasses: 60 - 15 = 45 girls do not wear glasses.
The probability of selecting a girl who does not wear glasses is found by taking the number of girls who do not wear glasses (45) and dividing it by the total number of students (100):
P(Girl does not wear glasses) = 45 / 100 = 0.45 = 45%.