Question

The two-way table shows the distribution of gender to favorite film genre for the senior class at Mt. Rose High School.

Answer 1

Answer:

The second statement is correct

Step-by-step explanation:

Hello!

The table shows the information of the favorite film genre of the students of the class regarding their gender.

You have to prove which statement is correct:

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

If you chose a student at random, you need to calculate the probability of its favorite genre being "Drama" (D) and the student being female (F), symbolically: P(D∩F)

To do so you have to divide the number of observed students that are female and like drama by the total number of students:

P(D∩F)= $\frac{24}{240}= \frac{1}{10} =0.10$

This means that the probability of choosing a student at random and it being a female that likes drama is 10%.

This statement is incorrect.

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

Two events are independent when the occurrence of one of them doesn't affect the probability of occurrence of the other one.

So if F and D are independent then:

P(F)= P(F|D)

-or-

P(D)=P(D|F)

The probability of the event "Female" is equal to $P(F)= \frac{Total females in the class}{n} = \frac{144}{240} = \frac{3}{5}= 0.6$

The probability of the event "Drama" is:

$P(D)= \frac{Total students that like "Drama"}{n}= \frac{40}{240}= \frac{1}{6}= 0.166$

$P(F|D)= \frac{P(FnD)}{P(D)}= \frac{\frac{1}{10} }{\frac{1}{6} }= \frac{3}{5} = 0.6$

As you can see P(F)= 0.6 and P(F|D)= 0.6 so both events are independent.

This statement is correct.

3) The probability of randomly selecting a male student, given that his favorite genre is horror, is  16/40

This is a conditional probability, you already know that the student likes horror movies (H), and out of that group you want to know the probability of the student being male (M):

$P(M|H)= \frac{number of male students that like horror movies}{total students that like horror movies}= \frac{16}{38}= \frac{8}{19} = 0.42$

This statement is incorrect.

4) Event M for male and event A for action are independent events.

Same as the second statement, if the events "Male" and "Action" are independent then:

P(M)= P(M|A)

-or-

P(A)= P(A|M)

$P(M)= \frac{96}{240}= \frac{2}{5}= 0.4$

$P(A)= \frac{72}{240} =\frac{3}{10}= 0.3$

$P(AnM)= \frac{28}{240}= \frac{7}{60}= 0.11666$

$P(M|A)= \frac{P(MnA)}{P(A)}= \frac{\frac{7}{60} }{\frac{3}{10} } = \frac{7}{18}= 0.3888$

$P(M)= \frac{2}{5}$ and $P(M|A)= \frac{7}{18}$

P(M)≠ P(M|A) the events are not independent.

This statement is incorrect.

I hope this helps!