Math Problem Statement

Giving a test to a group of students, the grades and gender are summarized below

A

B

C

Total

Male

5

15

7

27

Female

3

8

11

22

Total

8

23

18

49

If one student is chosen at random,

Find the probability that the student was male AND got a "B". Write your answer as a reduced fraction.

P(male and "B")=

Solution

To find the probability that a student was male and got a "B," we will use the formula for probability:

P(male and "B")=Number of males who got a "B"Total number of studentsP(\text{male and "B"}) = \frac{\text{Number of males who got a "B"}}{\text{Total number of students}}

Step-by-Step Solution:

  1. Number of males who got a "B" = 15
  2. Total number of students = 49

So, the probability is:

P(male and "B")=1549P(\text{male and "B"}) = \frac{15}{49}

The fraction 1549\frac{15}{49} is already in its simplest form, so the final answer is:

P(male and "B")=1549P(\text{male and "B"}) = \frac{15}{49}

Would you like further details, or do you have any questions?

Here are five related questions to explore:

  1. What is the probability of selecting a student who is female and got a "C"?
  2. What is the probability that a student got a grade of "A"?
  3. If a student is chosen randomly, what is the probability that the student is male?
  4. What is the probability that a student chosen randomly got a "B"?
  5. What is the probability that a student chosen at random is female?

Tip: When dealing with probability, always ensure fractions are reduced to their simplest form to make interpretation easier.

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Math Problem Analysis

Mathematical Concepts

Probability
Basic Fractions

Formulas

P(event) = Number of favorable outcomes / Total number of outcomes

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8