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 for the probability of the union of two events 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 given values into the formula

Substitute \( P(A) = 0.3 \), \( P(B) = 0.25 \), and \( P(A \text{ or } B) = 0.35 \) into the formula: \( P(A \text{ and } B) = 0.3 + 0.25 - 0.35 \).

Step4: Calculate the result

First, add \( 0.3 \) and \( 0.25 \): \( 0.3 + 0.25 = 0.55 \). Then subtract \( 0.35 \) from \( 0.55 \): \( 0.55 - 0.35 = 0.2 \), which is \( 20\% \).

Answer:

B. 20%