Question

The diagram below represents three groups of students:
S (blue and green): The set of students who took a Spanish class.
T (green and orange): The set of students who traveled to a Spanish-speaking country.
D (red and orange): The set of students who did not take a Spanish class. Each block represents one student.

How many times more likely is it for a student who took Spanish to have traveled to a Spanish-speaking country than a student who did not take Spanish?
a. It is 2.3 times as likely.
b. It is 3.3 times as likely.
c. It is 23 times as likely.
d. It is 30 times as likely.

Answer 1

The data is shown in the Venn diagram below

The probability of students traveling to Spain GIVEN that they took Spanish Class is 8 out of 24

The probability of students traveling to Spain GIVEN they did not take Spanish class is 8 out of 80

Hence the probability that a student travels to Spain given that the student took Spanis class is $\frac{1}{3}$÷$\frac{1}{10}$=$\frac{10}{3}$ or 3.33 times likely