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.\nwhat is the probability that a student chooses drama as an elective?\no 5 percent\no 7 percent\no 33 percent\no 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.\nwhat is the probability that a student chooses drama as an elective?\no 5 percent\no 7 percent\no 33 percent\no 37 percent

Answer

Answer:

B. 7 percent

Explanation:

Step1: Recall probability formula

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$ Let $A$ be the event of choosing art and $B$ be the event of choosing drama. We know $P(A) = 0.15$, $P(A\cup B)=0.20$ and $P(A\cap B)=0.02$.

Step2: Rearrange formula to solve for $P(B)$

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

Step3: Substitute values

$P(B)=0.20 + 0.02-0.15$ $P(B)=0.07$ or 7 percent.