Probability of choosing both students are not boy

In summary, the probability of choosing both students are not boy refers to the likelihood that two randomly chosen students from a group will both be of a gender other than male. This is calculated by taking the number of non-boy students in the group and dividing it by the total number of students, then multiplying that probability by itself. Factors that can influence this probability include the gender distribution of the group and chance. The size of the group can also affect the probability, as a larger group provides more options for non-boy students to be chosen from. While the probability can never be exactly 0, it can be extremely low in cases where there are no non-boy students in the group.
  • #1
desmond iking
284
2

Homework Statement


A class consists of 25 boys and 15 girls . Two students are selected randomly. what is the probablity of both students are not boys?


Homework Equations





The Attempt at a Solution



my working is (15C1 X 14C1) /(40C1 x 39C1) = 7/52

or 15/40 x 14/39 = 7/52


but the ans is 8/13
 
Physics news on Phys.org
  • #2
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"!)
 
  • Like
Likes 1 person
  • #3
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"!)

by considering case i and case ii , and then add up the bth probability i got the ans of 8/13 finally.

i misunderstood the question so i ended up getting the probability of both are girls only.
 
  • #4
An easier way to look at it: The complement of the event "both selected students are not boys" is "both selected students are boys". The sum of the probabilities of these two complementary events must be one. The probability that both selected students are boys is easily computed: It's 25/40 * 24/39 = 5/13. The probability that both selected students are not boys is thus 1-5/13, or 8/13.
 

FAQ: Probability of choosing both students are not boy

1. What does "probability of choosing both students are not boy" mean?

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.

2. How is the probability of choosing both students are not boy calculated?

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.

3. What factors can influence the probability of choosing both students are not boy?

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.

4. Is the probability of choosing both students are not boy affected by the size of the group?

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.

5. Can the probability of choosing both students are not boy ever be 0?

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.

Back
Top