Subjects probability

Conditional Probability 6268Ac

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1. **State the problem:** We want to find the probability that a student is male given that the student has an A in the class. 2. **Identify the data from the table:** - Number of females with an A: 9 - Number of males with an A: 2 - Number of females without an A: 5 - Number of males without an A: 10 3. **Recall the formula for conditional probability:** $$P(\text{Male} \mid \text{Has an A}) = \frac{P(\text{Male and Has an A})}{P(\text{Has an A})}$$ 4. **Calculate the numerator:** Number of males with an A = 2 5. **Calculate the denominator:** Total number of students with an A = Number of females with an A + Number of males with an A = 9 + 2 = 11 6. **Calculate the conditional probability:** $$P(\text{Male} \mid \text{Has an A}) = \frac{2}{11}$$ 7. **Final answer:** The probability that a student is male given that they have an A is $$\boxed{\frac{2}{11}}$$.