a guidance counselor reports that in a given semester, the probability that a student chooses art as an…

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? 5 percent 7 percent 33 percent 37 percent

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? 5 percent 7 percent 33 percent 37 percent

Answer

Explanation:

Step1: Recall the formula for probability of union

Let $P(A)$ be the probability of choosing art, $P(D)$ be the probability of choosing drama, and $P(A\cup D)$ be the probability of choosing art or drama, $P(A\cap D)$ be the probability of choosing both art and drama. The formula is $P(A\cup D)=P(A)+P(D)-P(A\cap D)$.

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

We can rewrite the formula as $P(D)=P(A\cup D)+P(A\cap D)-P(A)$.

Step3: Substitute the given values

We know that $P(A) = 0.15$, $P(A\cup D)=0.20$, and $P(A\cap D)=0.02$. Substituting these values into the formula: $P(D)=0.20 + 0.02-0.15$.

Step4: Calculate the result

$P(D)=0.07$.

Answer:

7 percent