Question

the two - way table shows the distribution of gender to favorite film genre for the senior class at mt. rose high school. which statement is true? the probability of randomly selecting a student who has a favorite genre of drama and is also female is about 17 percent. event f for female and event d for drama are independent events. the probability of randomly selecting a male student, given that his favorite genre is horror, is 16/40. event m for male and event a for action are independent events.

Explanation:

Step1: Calculate probability for first option

The number of students who like drama and are female is \(24\). Total number of students is \(240\). Probability \(P=\frac{24}{240}=0.1 = 10\%
eq17\%\)

Step2: Check independence for second option

\(P(F)=\frac{144}{240}=0.6\), \(P(D)=\frac{40}{240}=\frac{1}{6}\approx0.167\), \(P(F\cap D)=\frac{24}{240} = 0.1\). \(P(F)\times P(D)=0.6\times\frac{1}{6}=0.1 = P(F\cap D)\). But let's check other options too.

Step3: Calculate conditional probability for third option

Number of students who like horror is \(38\). Number of male students who like horror is \(16\). Conditional probability \(P(M|H)=\frac{16}{38}=\frac{8}{19}
eq\frac{16}{40}\)

Step4: Check independence for fourth option

\(P(M)=\frac{96}{240}=0.4\), \(P(A)=\frac{72}{240}=0.3\), \(P(M\cap A)=\frac{28}{240}\approx0.117\). \(P(M)\times P(A)=0.4\times0.3 = 0.12
eq0.117\)

Answer:

Event \(F\) for female and event \(D\) for drama are independent events.