Math Problem Statement

After giving a test to a group of students, below is the summary of grades by gender.

A B C Total Male 13 9 7 29 Female 8 5 20 33 Total 21 14 27 62

If a student was randomly chosen, find the probability that the student earned a C. Leave your answer as a reduced fraction.

Solution

To find the probability that a randomly chosen student earned a grade of C, we need to focus on the total number of students who earned a C and divide that by the total number of students in the group.

Here is the breakdown:

  • Total number of students who earned a C: 2727 (both male and female).
  • Total number of students in the group: 6262.

Thus, the probability P(C)P(C) that a randomly chosen student earned a C is:

P(C)=Number of students who earned a CTotal number of students=2762P(C) = \frac{\text{Number of students who earned a C}}{\text{Total number of students}} = \frac{27}{62}

The fraction 2762\frac{27}{62} is already in its simplest form because 27 and 62 have no common factors other than 1.

So, the probability that a randomly chosen student earned a C is:

2762\boxed{\frac{27}{62}}

Would you like further clarification or details? Here are some related questions to consider:

  1. What is the probability that a randomly chosen student is male?
  2. What is the probability that a randomly chosen student is female?
  3. What is the probability that a randomly chosen student earned an A?
  4. What is the probability that a randomly chosen male student earned a B?
  5. What is the probability that a randomly chosen female student earned an A?

Tip: When calculating probabilities, always ensure the total number of possible outcomes is correct to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Probability
Fractions
Ratios

Formulas

P(Event) = Number of Favorable Outcomes / Total Number of Outcomes

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8