Question

analyzing a two-way table

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 \\(\frac{16}{40}\\).
• event m for male and event a for action are independent events.

Explanation:

Analyze the given two-way table

Using the Two-Way Frequency Tables knowledge point

• Total number of students: \(N = 240\)
• Total males: \(P(M) = \frac{96}{240} = 0.4\)
• Total females: \(P(F) = \frac{144}{240} = 0.6\)
• Total drama: \(P(D) = \frac{40}{240} \approx 0.1667\)
• Total horror: \(P(H) = \frac{38}{240} \approx 0.1583\)
• Total action: \(P(A) = \frac{72}{240} = 0.3\)

Evaluate the first statement

Using the Two-Way Frequency Tables knowledge point

• Female and Drama count: \(24\)
• Probability: \(P(F \cap D) = \frac{24}{240} = 0.10 = 10\%\)
• The statement claims it is about \(17\%\), which is incorrect.

Evaluate the second statement

Using the Independent Events knowledge point

$$
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Evaluate the third statement

Using the Conditional Probability Calculation knowledge point

$$ P(M \mid H) = \frac{\text{Male and Horror}}{\text{Total Horror}} = \frac{16}{38} $$

• The statement claims the probability is \(\frac{16}{40}\), which is incorrect.

Evaluate the fourth statement

Using the Independent Events knowledge point

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Answer:

• 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. (Correct answer)
• The probability of randomly selecting a male student, given that his favorite genre is horror, is \(\frac{16}{40}\).
• Event M for male and event A for action are independent events.