HallsofIvy said:Do you mean "both students are not boys" which is the same as "both are girls" or do you mean "the students are not both boys" which means at "least one is a girl"
In either case, your working is much too complicated. It looks like you are trying to apply formulas rather than thinking about the problem.
Assuming you meant the first then there are originally 40 students, 15 of whom are girls. The probability the first student chosen is a girl is 15/40= 3/8. There are then 39 students, 14 of whom are girls. What is the probability the second chosen is a girl? What is the probability both are girls?
Assuming you mean the second then there are originally 40 students, 15 of whom are girls. The probability the first student chosen is a girl is 15/40= 3/8. There are then 39 students, 25 of whom are boys. What is the probability the second chosen is a boy? What is the probability of "girl, boy", in that order?
Of course, then we have to compute the other order- there are originally 40 students, 25 of whom are boys. The probability the first student chosen is a boy is 25/40= 5/8. There are then 39 students, 15 of whom are girls. What is the probability the second chosen is a girl? What is the probability of "boy, girl", in that order?
What is the probability of "boy, girl" in either order?
(In either case, the answer is NOT "8/13"!)
The probability of choosing both students are not boy refers to the likelihood that, out of a given group of students, two randomly chosen students will both be of a gender other than male.
The probability of choosing both students are not boy is calculated by taking the number of students who are not boys in the group and dividing it by the total number of students in the group. This gives the probability of choosing one non-boy student. Then, the probability is multiplied by itself to find the probability of choosing two non-boy students in a row.
The probability of choosing both students are not boy can be influenced by the gender distribution of the group of students. If there are more non-boy students in the group, the probability will be higher. Additionally, if the group is randomly selected, the probability will also be affected by chance.
Yes, the size of the group can affect the probability of choosing both students are not boy. The larger the group, the higher the probability of choosing two non-boy students, as there are more options for non-boy students to be chosen from.
No, the probability of choosing both students are not boy can never be exactly 0. Even if there are no non-boy students in the group, there is still a chance that two non-boy students could be chosen by chance. However, the probability can be extremely low in this scenario.