Question

use the information about student enrollment in two classes and the formula. 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 probabilities

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

Step2: Rearrange the formula

We know $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$. Rearranging for $P(A\ and\ B)$ gives $P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)$.

Step3: Substitute values

$P(A\ and\ B)=0.3 + 0.25- 0.35$.
$P(A\ and\ B)=0.2$ or $20\%$.

Answer:

B. 20%