to get to know her students better, ms. williamson surveyed her math students to determine what hobbies and…

to get to know her students better, ms. williamson surveyed her math students to determine what hobbies and school subjects they prefer. athletics the arts math 4 3 literature 4 3 are the events \the student prefers literature\ and \the student prefers athletics\ independent? yes no

to get to know her students better, ms. williamson surveyed her math students to determine what hobbies and school subjects they prefer. athletics the arts math 4 3 literature 4 3 are the events \the student prefers literature\ and \the student prefers athletics\ independent? yes no

Answer

Explanation:

Step1: Calculate total number of students

Total students = 4 + 3+ 4 + 3 = 14

Step2: Calculate probability of preferring literature

P(Literature)=$\frac{4 + 3}{14}=\frac{7}{14}=\frac{1}{2}$

Step3: Calculate probability of preferring athletics

P(Athletics)=$\frac{4+4}{14}=\frac{8}{14}=\frac{4}{7}$

Step4: Calculate probability of preferring both literature and athletics

P(Literature and Athletics)=$\frac{4}{14}=\frac{2}{7}$

Step5: Check independence condition

If two events A and B are independent, P(A and B)=P(A)×P(B). Here, P(Literature)×P(Athletics)=$\frac{1}{2}\times\frac{4}{7}=\frac{2}{7}$, and P(Literature and Athletics) = $\frac{2}{7}$. Since P(Literature and Athletics)=P(Literature)×P(Athletics), the events are independent.

Answer:

yes