Question

35% of students take spanish or engineering
30% of students take spanish
25% of students take engineering
$p(a \text{ or } b) = p(a) + p(b) - p(a \text{ and } b)$
what is the probability that a student takes spanish and engineering?
\\(\bigcirc\\) a. 15%
\\(\bigcirc\\) b. 20%
\\(\bigcirc\\) c. 25%
\\(\bigcirc\\) d. 30%
\\(\bigcirc\\) e. 40%

Explanation:

Step1: Identify the formula and values

We use the formula for the probability of the union of two events: \( P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \). Let \( A \) be the event that a student takes Spanish and \( B \) be the event that a student takes Engineering. We know \( P(A \text{ or } B) = 35\% = 0.35 \), \( P(A) = 30\% = 0.30 \), and \( P(B) = 25\% = 0.25 \). We need to find \( P(A \text{ and } B) \).

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

Rearranging the formula gives \( P(A \text{ and } B) = P(A) + P(B) - P(A \text{ or } B) \).

Step3: Substitute the values into the formula

Substitute \( P(A) = 0.30 \), \( P(B) = 0.25 \), and \( P(A \text{ or } B) = 0.35 \) into the formula:
\( P(A \text{ and } B) = 0.30 + 0.25 - 0.35 \)
\( P(A \text{ and } B) = 0.55 - 0.35 \)
\( P(A \text{ and } B) = 0.20 \) or \( 20\% \)

Answer:

B. 20%