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)= [tex]\frac{24}{240}= \frac{1}{10} =0.10[/tex]
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 [tex]P(F)= \frac{Total females in the class}{n} = \frac{144}{240} = \frac{3}{5}= 0.6[/tex]
The probability of the event "Drama" is:
[tex]P(D)= \frac{Total students that like "Drama"}{n}= \frac{40}{240}= \frac{1}{6}= 0.166[/tex]
[tex]P(F|D)= \frac{P(FnD)}{P(D)}= \frac{\frac{1}{10} }{\frac{1}{6} }= \frac{3}{5} = 0.6[/tex]
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):
[tex]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[/tex]
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)
[tex]P(M)= \frac{96}{240}= \frac{2}{5}= 0.4[/tex]
[tex]P(A)= \frac{72}{240} =\frac{3}{10}= 0.3[/tex]
[tex]P(AnM)= \frac{28}{240}= \frac{7}{60}= 0.11666[/tex]
[tex]P(M|A)= \frac{P(MnA)}{P(A)}= \frac{\frac{7}{60} }{\frac{3}{10} } = \frac{7}{18}= 0.3888[/tex]
[tex]P(M)= \frac{2}{5}[/tex] and [tex]P(M|A)= \frac{7}{18}[/tex]
P(M)≠ P(M|A) the events are not independent.
This statement is incorrect.
I hope this helps!
