Math Problem Statement

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

Grades vs. Gender   ABCMale

5

9

10

Female

11

17

8

If one student was chosen at random, find the probability that the student was male.

Probability =  (Round to 4 decimal places)

Solution

To find the probability that a randomly chosen student is male, we need to use the formula for probability:

P(Male)=Number of Male StudentsTotal Number of StudentsP(\text{{Male}}) = \frac{\text{{Number of Male Students}}}{\text{{Total Number of Students}}}

Step 1: Determine the number of male students.

From the table:

  • Male students with grade A = 5
  • Male students with grade B = 9
  • Male students with grade C = 10

Total number of male students:

5+9+10=245 + 9 + 10 = 24

Step 2: Determine the number of female students.

From the table:

  • Female students with grade A = 11
  • Female students with grade B = 17
  • Female students with grade C = 8

Total number of female students:

11+17+8=3611 + 17 + 8 = 36

Step 3: Calculate the total number of students.

24+36=6024 + 36 = 60

Step 4: Calculate the probability.

P(Male)=2460=0.4P(\text{{Male}}) = \frac{24}{60} = 0.4

Thus, the probability that the randomly chosen student is male is:

0.4000\boxed{0.4000}

Would you like more details or have any questions?

Here are 5 related questions you could explore:

  1. What is the probability that the student has a grade of A?
  2. What is the probability that the student is female?
  3. What is the probability that a male student has a grade of C?
  4. What is the probability that a female student has a grade of B?
  5. If two students are chosen randomly, what is the probability that both are male?

Tip: Probabilities are always between 0 and 1. If your result is higher or lower, double-check your calculations!

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Math Problem Analysis

Mathematical Concepts

Probability
Basic Statistics

Formulas

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

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8