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).