Question

The probability that a student is a sophomore or a male is 0.55. The probability that a student is a sophomore is 0.32. The probability that a student is a male is 0.41. What is the probability that a student is a sophomore and male?

A.
0.13


B.
0.18


C.
0.45


D.
0.73

Answer 1

To find the probability that a student is both a sophomore and male, 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:
- \( P(A \cup B) \) is the probability that a student is a sophomore or male.
- \( P(A) \) is the probability that a student is a sophomore.
- \( P(B) \) is the probability that a student is male.
- \( P(A \cap B) \) is the probability that a student is both a sophomore and male.

From the problem:
- \( P(A \cup B) = 0.55 \)
- \( P(A) = 0.32 \)
- \( P(B) = 0.41 \)

Now we can rearrange the formula to solve for \( P(A \cap B) \):

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

Substituting in the values:

\[
P(A \cap B) = 0.32 + 0.41 - 0.55
\]

Calculating this gives:

\[
P(A \cap B) = 0.73 - 0.55 = 0.18
\]

Thus, the probability that a student is a sophomore and male is \( 0.18 \).

The answer is:

**B. 0.18**