Question

use the information about student enrollment in two classes and the formula shown to answer the question.
35% of students take spanish or engineering
30% of students take spanish
25% of students take engineering
p(a or b) = p(a) + p(b) − p(a and b)
what is the probability that a student takes spanish and engineering?
a. 15%
b. 20%
c. 25%
d. 30%
e. 40%

Explanation:

Step1: Identify given values

Let \( A \) be the event that a student takes Spanish, \( P(A) = 30\% = 0.3 \). Let \( B \) be the event that a student takes Engineering, \( P(B) = 25\% = 0.25 \). The probability that a student takes Spanish or Engineering is \( P(A \text{ or } B) = 35\% = 0.35 \).

Step2: Use the formula to solve for \( P(A \text{ and } B) \)

The formula is \( P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \). We need to solve for \( P(A \text{ and } B) \), so rearrange the formula:
\( P(A \text{ and } B) = P(A) + P(B) - P(A \text{ or } B) \)

Substitute the known values:
\( P(A \text{ and } B) = 0.3 + 0.25 - 0.35 \)

Step3: Calculate the result

First, add \( 0.3 \) and \( 0.25 \): \( 0.3 + 0.25 = 0.55 \)
Then subtract \( 0.35 \) from \( 0.55 \): \( 0.55 - 0.35 = 0.2 \)
Convert \( 0.2 \) to a percentage: \( 0.2 \times 100\% = 20\% \)

Answer:

B. 20%