Question

a guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent. what is the probability that a student chooses drama as an elective? \bigcirc 5 percent \bigcirc 7 percent \bigcirc 33 percent \bigcirc 37 percent

Explanation:

Step1: Recall addition rule for probability

For events A (art) and D (drama):
$$P(A \cup D) = P(A) + P(D) - P(A \cap D)$$

Step2: Rearrange to solve for $P(D)$

$$P(D) = P(A \cup D) - P(A) + P(A \cap D)$$

Step3: Substitute given values

$P(A \cup D)=20\%$, $P(A)=15\%$, $P(A \cap D)=2\%$
$$P(D) = 20\% - 15\% + 2\%$$

Step4: Calculate the result

$$P(D) = 7\%$$

Answer:

B. 7 percent