**An exam was given to a group of freshman and sophomore students. The results are summarized below:**



**A**

**B**

**C**

**Freshman**

124

165

110

**Sophomore**

156

191

180


**If one student is chosen at random from those who took the exam, find the probability that:**
*Round all answers to 4 decimal places as needed*

**a)The student was a sophomore.**

To find the probability that a randomly chosen student was a sophomore, we start by finding the total number of students who took the exam and the total number of sophomores.

### Step 1: Find the total number of students

\[
\text{Total Freshmen} = 124 + 165 + 110 = 399
\]
\[
\text{Total Sophomores} = 156 + 191 + 180 = 527
\]
\[
\text{Total Students} = \text{Total Freshmen} + \text{Total Sophomores}
\]
\[
\text{Total Students} = 399 + 527 = 926
\]

### Step 2: Calculate the probability

The probability that the student chosen was a sophomore is given by:

\[
P(\text{Sophomore}) = \frac{\text{Total Sophomores}}{\text{Total Students}} = \frac{527}{926}
\]

Let's calculate this value:

The probability that a randomly chosen student was a sophomore is **0.5691**.

Do you want any further details or have any questions?

Here are 5 related questions that build on this concept:
1. What is the probability that the chosen student was a freshman?
2. What is the probability that a student chosen was a sophomore who got a B?
3. What is the probability that a randomly chosen student got a grade C, regardless of their year?
4. If two students are chosen at random, what is the probability that both are sophomores?
5. What is the probability that a chosen student is a freshman and received an A?

**Tip:** When dealing with probability questions, always make sure to clearly define the total population or sample space first!

An exam was given to a group of freshman and sophomore students. The results are summarized below: Freshman: A=124, B=165, C=110; Sophomore: A=156, B=191, C=180. If one student is chosen at random from those who took the exam, find the probability that the student was a sophomore. Round all answers to 4 decimal places as needed.

Find the probability of selecting a sophomore from a group of freshmen and sophomores who took an exam. The problem covers key probability concepts and uses basic statistical formulas. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation