Question

The probability that a student is in the band, or a freshman, is .25. The probability that a student is a freshman is .31. The probability that a student is in the band is .08. What is the probability that the student is in the band and a freshman?
Hint:

P(A) + P(B) – P(A + B)
Group of answer choices

68%

14%

22%

6%

Answer 1

To find the probability that a student is in the band and a freshman, we can use the formula provided in the hint:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

Where:
- \( P(A \cup B) \) is the probability that a student is in the band or a freshman (given as 0.25).
- \( P(A) \) is the probability that a student is in the band (given as 0.08).
- \( P(B) \) is the probability that a student is a freshman (given as 0.31).
- \( P(A \cap B) \) is the probability that a student is both in the band and a freshman, which we want to find.

Now, we plug in the known values into the formula:

\[
0.25 = 0.08 + 0.31 - P(A \cap B)
\]

Simplifying the equation:

\[
0.25 = 0.39 - P(A \cap B)
\]
\[
P(A \cap B) = 0.39 - 0.25
\]
\[
P(A \cap B) = 0.14
\]

To convert the probability into a percentage, we multiply by 100:

\[
P(A \cap B) = 0.14 \times 100 = 14\%
\]

So the probability that the student is in the band and a freshman is **14%**. Thus, the correct answer is:

**14%**.