Question

PLEASE HELP!

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 1

Answer:

7 percent

Step-by-step explanation:

We have the following information from the question:

The probability that a student chooses art as an elective is 15 percent: $P(A)=15\%$

The probability that a student chooses art or drama is 20 percent: $P(A\cup D)=20\%$

The probability that a student chooses both art and drama is 2 percent:

$P(A\cap D)=2\%$

Recall that:

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

We plug in the various probabilities to get:

$20\%=15\%+P(D)-2\%$

$20\%-15\%+2\%=P(D)$

$7\%=P(D)$

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

Hence the probability that a student chooses drama as an elective is 7 percent

Answer 2

The probability that a student chooses drama as an elective is 7%

Represent the events as follows:

A represents Art

D represents Drama.

So, we have:

P(A) = 15%

P(A or D) = 20%

P(A and B) = 2%

The relationship between the probability values is:

P(A or D) = P(A) + P(D) - P(A and D)

So, we have:

20% = 15% + P(D) - 2%

Collect like terms

P(D) = 20% - 15% + 2%

Evaluate

P(D) = 7%

Hence, the probability that a student chooses drama as an elective is 7%

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