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, \( B \) be the event that a student takes Engineering. We know \( P(A \text{ or } B) = 35\% = 0.35 \), \( P(A) = 30\% = 0.3 \), \( P(B) = 25\% = 0.25 \). The formula is \( P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \).

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

We can rearrange the formula as \( P(A \text{ and } B) = P(A) + P(B) - P(A \text{ or } B) \).

Step3: Substitute the values into the formula

Substitute \( P(A) = 0.3 \), \( P(B) = 0.25 \), and \( P(A \text{ or } B) = 0.35 \) into the rearranged formula:
\( P(A \text{ and } B) = 0.3 + 0.25 - 0.35 \)
\( P(A \text{ and } B) = 0.55 - 0.35 \)
\( P(A \text{ and } B) = 0.2 \)
Convert \( 0.2 \) to a percentage: \( 0.2\times100\% = 20\% \).

Answer:

B. 20%