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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

Question

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frika frika · Answer 1 · 2018-12-24T23:27:13+01:00

Answer:

Correct choice is B

Step-by-step explanation:

Events A and B are independent then

[tex]Pr(A\cap B)=Pr(A)\cdot Pr(B).[/tex]

Consider events F and D:

[tex]Pr(F)=\dfrac{144}{240}=\dfrac{12}{20}=\dfrac{6}{10};[/tex]

[tex]Pr(D)=\dfrac{40}{240}=\dfrac{1}{6};[/tex]

[tex]Pr(F\cap D)=\dfrac{24}{240}=\dfrac{1}{10}.[/tex]

Note that

[tex]Pr(F)\cdot Pr(D)=\dfrac{6}{10}\cdot \dfrac{1}{6}=\dfrac{1}{10}=Pr(F\cap D).[/tex]

This means that events F and D are independent.

swapnalimalwadeVT swapnalimalwadeVT · Answer 2 · 2022-05-03T13:39:36+02:00

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

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

An independent event is an event that has no connection to another event's chances of happening (or not happening).

Events A and B are independent then

[tex]P(A\cap B)=P(A) \times P(B)[/tex]

Consider events F and D:

[tex]Pr(F)=\frac{144}{240} =\frac{12}{20}=\frac{6}{10}[/tex]

[tex]Pr(D)=\frac{40}{240}=\frac{1}{6}[/tex]

[tex]Pr(F\cap D)=\frac{24}{240}=\frac{1}{10}[/tex]

Note that,

[tex]P(F) \times P(D)=\frac{6}{10} \times \frac{1}{6} =\frac{1}{10}[/tex]

This means that events F and D are independent.

To learn more about the independent visit:

https://brainly.com/question/25223322#SPJ3