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

Explanation:

Step1: Calculate probability of female - drama

Find number of female - drama students (24) and total students (240). Probability $P=\frac{24}{240}= 0.1 = 10%$, so first statement is false.

Step2: Check independence of F and D

$P(F)=\frac{144}{240}$, $P(D)=\frac{40}{240}$, $P(F\cap D)=\frac{24}{240}$. $P(F)\times P(D)=\frac{144}{240}\times\frac{40}{240}=\frac{144\times40}{240\times240}=\frac{5760}{57600}= 0.1$ and $P(F\cap D) = 0.1$. Since $P(F\cap D)=P(F)\times P(D)$, F and D are independent events.

Step3: Calculate conditional probability of male - horror

Number of male - horror students is 16 and number of horror - loving students is 38. Probability $P=\frac{16}{38}=\frac{8}{19}\neq\frac{16}{40}$, so third statement is false.

Step4: Check independence of M and A

$P(M)=\frac{96}{240}$, $P(A)=\frac{72}{240}$, $P(M\cap A)=\frac{28}{240}$. $P(M)\times P(A)=\frac{96}{240}\times\frac{72}{240}=\frac{96\times72}{240\times240}=\frac{6912}{57600}= 0.12$ and $P(M\cap A)=\frac{28}{240}\approx0.117$. Since $P(M\cap A)\neq P(M)\times P(A)$, M and A are not independent events.

Answer:

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