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

Answer

Explanation:

Step1: Recall the formula for the probability of the union of two events

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

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

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

Step3: Substitute the known values

$P(B)=0.20 - 0.15+0.02$ $P(B)=0.07$

Answer:

7 percent