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? 5 percent 7 percent 33 percent 37 percent

Explanation:

Step1: Recall the formula for the probability of the union

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $A$ is the event of choosing art and $B$ is the event of choosing drama. Let $P(A) = 15\%=0.15$, $P(A\cup B)=20\% = 0.2$, and $P(A\cap B)=2\%=0.02$.

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

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

Step3: Substitute the values

Substitute the given values into the formula: $P(B)=0.2 - 0.15+0.02$.
$P(B)=0.07$ or 7 percent.

Answer:

7 percent