# Basic probability question

• BCCB
In summary, the conversation discusses the expected number of students who are not enrolled in sports on a bus carrying 500 students, with two different wordings of the problem resulting in the same answer of 25. The first wording states that 5% of the students on the bus are not enrolled in sports, while the second states that 5% of all students at the school are not enrolled in sports. The clarification is made that the expected value is 25, but the actual number may vary.

#### BCCB

Hi, I have a quick question

5% of students on a school bus are not enrolled in sports. If there are 500 students on a bus. What is the expected numbers of students who are not enrolled in sports on any given bus?

So, 5%(500)=25??

is this correct? Thanks

That's one hell of a big bus ! Yes, the math looks correct.

hehehe yes I suppose it is quite a large bus!

would the solution change at all if it were worded as "5% of students all students are not enrolled in sports"...?

thanks

BCCB said:
hehehe yes I suppose it is quite a large bus!

would the solution change at all if it were worded as "5% of students all students are not enrolled in sports"...?

thanks

I don't understand that wording at all so have no idea what it means.

sorry, 5% of all students are not enrolled in sports. If there are 500 students on a bus. What is the expected numbers of students who are not enrolled in sports on any given bus?

BCCB said:
sorry, 5% of all students are not enrolled in sports. If there are 500 students on a bus. What is the expected numbers of students who are not enrolled in sports on any given bus?

Why would you expect this to give a different answer than your original wording? If you were asking about students NOT on the bus, the answers might be different, but this looks the same.

The difference between your first and second statement of the problem is conceptual only: the answer in each case is 25.
In the first case nothing is random: you are told the number of students on a bus, and told that 5% of them do not play sports. In this case you know that 500 times 5%, or 25, of the students are not in sports.

If I understand your second version, you are told that 5% of all students at the school do not play sports, and then are asking how many of the 500 on the bus you can expect not to be in sports. If you make the assumption that the students on the bus are a representative sample of all students in the school, then the number on the bus who are not in sports is binomial, with n = 500 and p = .05, so the expected number is again 25.

The difference is in interpretation: in the first posing we KNOW the number is 25, the second is the number in an expected value.

thanks for the clarification, I understand it now

But as I drive to work to day, I will keep an eye out for that 500 passenger bus!