the 154 tenth - graders at wilson high school were polled on whether they enjoyed their algebra or geometry…

Explanation:

Step1: Calculate total number of males

Add the number of males who prefer algebra and geometry. Total males = 33 + 47 = 80. Total students = 154.

Step2: Calculate probability of choosing a male

Probability = $\frac{\text{Number of males}}{\text{Total number of students}}$. So, $P(\text{male})=\frac{80}{154}=\frac{40}{77}$.

Step3: Calculate number of students who prefer geometry

Total students who prefer geometry = 40 + 47 = 87.

Step4: Calculate probability of male given geometry preference

$P(\text{male}|\text{geometry})=\frac{\text{Number of males who prefer geometry}}{\text{Total number of students who prefer geometry}}=\frac{47}{87}$.

Step5: Check for independence

Two events A and B are independent if $P(A|B)=P(A)$. Here, $P(\text{male})=\frac{40}{77}\approx0.519$ and $P(\text{male}|\text{geometry})=\frac{47}{87}\approx0.540$. Since $P(\text{male})\neq P(\text{male}|\text{geometry})$, the events are not independent.

Answer:

What is the probability that a randomly - chosen tenth - grader is male? $\frac{40}{77}$ What is the probability that a randomly chosen tenth - grader is male given that the tenth - grader prefers geometry? $\frac{47}{87}$ Are the events "male" and "geometry" independent? No