the two - way table shows the distribution of gender to favorite film genre for the senior class at mt. rose…

Answer:

The probability of randomly selecting a student who has a favorite genre of drama and is also female is about 17 percent.

Explanation:

Step1: Calculate the probability

The number of female students who like drama is 24, and the total number of students is 240. The probability $P=\frac{24}{240}= 0.1 = 10%$. This statement is false.

Step2: Check independence for F and D

$P(F)=\frac{144}{240}=0.6$, $P(D)=\frac{40}{240}=\frac{1}{6}$, $P(F\cap D)=\frac{24}{240} = 0.1$. Since $P(F)\times P(D)=0.6\times\frac{1}{6}=0.1 = P(F\cap D)$, event F for female and event D for drama are independent events. This statement is true.

Step3: Calculate conditional - probability for male and horror

The number of male students who like horror is 16, and the number of students who like horror is 38. The probability of randomly selecting a male student, given that his favorite genre is horror, is $P=\frac{16}{38}=\frac{8}{19}\neq\frac{16}{40}$. This statement is false.

Step4: Check independence for M and A

$P(M)=\frac{96}{240}=0.4$, $P(A)=\frac{72}{240}=0.3$, $P(M\cap A)=\frac{28}{240}\approx0.117$. Since $P(M)\times P(A)=0.4\times0.3 = 0.12\neq0.117 = P(M\cap A)$, event M for male and event A for action are not independent events. This statement is false.

So the true statement is "Event F for female and event D for drama are independent events."