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

Total males = 33 + 47 = 80 Total students = 154

Step2: Calculate probability that a randomly - chosen tenth - grader is male

$P(\text{male})=\frac{80}{154}=\frac{40}{77}$

Step3: Calculate number of students who prefer geometry

Total students who prefer geometry = 40 + 47 = 87 Number of males who prefer geometry = 47

Step4: Calculate probability that a tenth - grader is male given that they prefer geometry

$P(\text{male}|\text{geometry})=\frac{47}{87}$

Step5: Check for independence

Two events $A$ (being male) and $B$ (preferring geometry) are independent if $P(A)\times P(B)=P(A\cap B)$. $P(\text{male})\times P(\text{geometry})=\frac{80}{154}\times\frac{87}{154}=\frac{80\times87}{154\times154}=\frac{6960}{23716}$ $P(\text{male}\cap\text{geometry})=\frac{47}{154}$ Since $\frac{80}{154}\times\frac{87}{154}\neq\frac{47}{154}$, 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