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: Define variables

Let $P(A\ or\ B)$ be the probability of taking Spanish or Engineering, $P(A)$ be the probability of taking Spanish, $P(B)$ be the probability of taking Engineering, and $P(A\ and\ B)$ be the probability of taking both. Given $P(A\ or\ B)=35\% = 0.35$, $P(A)=30\%=0.3$, $P(B)=25\% = 0.25$.

Step2: Rearrange the formula

We have the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$. Rearranging it to solve for $P(A\ and\ B)$ gives $P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)$.

Step3: Substitute values

Substitute the known values into the formula: $P(A\ and\ B)=0.3 + 0.25- 0.35$.
$P(A\ and\ B)=0.2$ or $20\%$.

Answer:

B. 20%