Question

The probability that a student is in the school choir is 0.09. The probability that the student plays for the school basketball team is 0.08. If the probability that the student plays for the school basketball team and sings in the choice is 0.01, find the probability that the student sings in the choir or plays for the school basketball team. (Hint: Make a Venn diagram to help you organize the information.)

Question 8 options:

0.16


0.17


0.15

Answer 1

To find the probability that a student sings in the choir or plays for the school basketball team, we can use the formula for the probability of the union of two events:

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

Where:
- \( P(A) \) is the probability that a student is in the choir.
- \( P(B) \) is the probability that a student plays for the basketball team.
- \( P(A \cap B) \) is the probability that a student is both in the choir and on the basketball team.

Given:
- \( P(A) = 0.09 \)
- \( P(B) = 0.08 \)
- \( P(A \cap B) = 0.01 \)

Now we can substitute these values into the formula:

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

Calculating each term:
\[
P(A \cup B) = 0.09 + 0.08 - 0.01
\]

\[
P(A \cup B) = 0.17 - 0.01
\]

\[
P(A \cup B) = 0.16
\]

Thus, the probability that a student sings in the choir or plays for the school basketball team is **0.16**.

The correct answer is:
**0.16**