# Probability that the selected student will be in an odd-numbered grade

• vvvidenov
In summary, the school has equal number of students in grades 2,3,4,5,6 and twice this number in grade 1. The total population of the school is 7 times the number of students in grades 2,3,4,5 and 6. Therefore, the probability of randomly selecting a student from grade 3 is 1/7 and the probability of selecting a student from an odd-numbered grade is also 1/7.
vvvidenov

## Homework Statement

A school contains students in grades 1,2,3,4,5 and 6. Grades 2,3,4,5 and 6 all contain the same number of students, but there are twice this number in grade 1.

a)If a student is selected at random from a list of all the students in the school, what is the probability that he will be in grade 3?
b)What is the probability that the selected student will be in an odd-numbered grade?

## The Attempt at a Solution

Let n=the size of grade(s) 2,(3,4,5,6) then 2n=the size of grade 1.
So the size of the sample space I don't know how to find.
I really need help on this. I am not sure what to do from here at all. Thanks.

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This is really just testing how you work with variables. Since you have n = the size of grades 2,3,4,5,6, and 2n = size of grade 1, the school's population must be 2n + 5*n, where the 2n represents the size of grade 1, and the 5*n represents the size of grades greater than 1 (since there are 5 of them). Therefore, the population is 7n. Given this fact, how would you be able to find the probabilities of a) and b)?

ok, I see the response above.

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so the event (student chosen is in grade 3) has size=7
so the probability is =1/7

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## 1. What is probability?

Probability is a measure of the likelihood of an event occurring. It is represented as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

## 2. How is probability calculated?

Probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes. This is known as the probability formula: P(A) = desired outcomes / total outcomes.

## 3. What is an odd-numbered grade?

An odd-numbered grade refers to a grade level that is not divisible by 2, such as 1st, 3rd, 5th, etc. In other words, it is a grade that ends in the digits 1, 3, 5, 7, or 9.

## 4. How is the probability of being in an odd-numbered grade calculated?

The probability of a selected student being in an odd-numbered grade can be calculated by dividing the number of odd-numbered grades by the total number of grades. For example, if there are 6 odd-numbered grades (1st, 3rd, 5th, 7th, 9th, and 11th) out of a total of 12 grades, the probability would be 6/12 or 0.5.

## 5. What factors can affect the probability of a student being in an odd-numbered grade?

The main factor that affects the probability of a student being in an odd-numbered grade is the grade structure of the school or educational system. If the system follows a traditional structure with grades 1-12, the probability would be 6/12 or 0.5. However, if the system includes additional grades or follows a different structure, the probability may change.

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