Giving a test to a group of students, the table below summarizes the grade earned by gender.

 	A	B	C	Total
Male	12	19	2	33
Female	14	16	15	45
Total	26	35	17	78

If one student is chosen at random, find the probability that the student is male given the student earned grade B. Round your answer to four decimal places.

The problem is asking for the probability that a randomly chosen student is male, given that the student earned a grade of B. This is a conditional probability problem.

The formula for conditional probability is:

\[
P(\text{Male | Grade B}) = \frac{P(\text{Male and Grade B})}{P(\text{Grade B})}
\]

From the table, we can extract the necessary information:

- **P(Male and Grade B)**: This is the number of male students who earned a B, which is 19.
- **P(Grade B)**: This is the total number of students who earned a B, which is 35.

Now, we calculate the conditional probability:

\[
P(\text{Male | Grade B}) = \frac{19}{35}
\]

Next, we compute the value and round to four decimal places:

\[
P(\text{Male | Grade B}) = 0.5429
\]

Thus, the probability that a randomly chosen student is male given that they earned a grade of B is **0.5429**.

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

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Here are 5 related questions to expand on the concept:

1. What is the probability that a randomly chosen student earned grade B given they are female?
2. What is the probability that a randomly chosen student is female given that the student earned grade C?
3. What is the total probability that a randomly chosen student earned an A?
4. How would the probability change if more male students had earned grade C?
5. How do we calculate the probability that a student is female and earned an A?

**Tip**: Always make sure to carefully distinguish between joint probabilities (both events happening) and conditional probabilities (one event given another).

Giving a test to a group of students, the table below summarizes the grade earned by gender. If one student is chosen at random, find the probability that the student is male given the student earned grade B. Round your answer to four decimal places.

A   B   C   Total
Male   12  19  2   33
Female 14  16  15  45
Total  26  35  17  78

Learn how to calculate the conditional probability that a randomly chosen student is male given that they earned grade B. Using a table with grades for male and female students, this problem demonstrates the use of conditional probability formulas. Suitable for students in Grades 9-12.

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