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 the formula and values

The formula is \(P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)\). Let \(A\) be Spanish and \(B\) be Engineering. \(P(A\ or\ B) = 35\%\), \(P(A)=30\%\), \(P(B) = 25\%\).

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

From \(P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)\), we can get \(P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)\).

Step3: Substitute the values

Substitute \(P(A) = 30\%\), \(P(B)=25\%\), \(P(A\ or\ B)=35\%\) into the formula: \(P(A\ and\ B)=30\%+25\% - 35\%\).

Step4: Calculate

\(30\%+25\% - 35\%=(30 + 25-35)\%=20\%\).

Answer:

B. 20%