A college has 500 students. A survey has determined that:72 read French 40 read German 39 read Spanish 18 read French and German 18 read French and Spanish 9 read German and Spanish 6 read all three languages. Put this information into a venn diagram and use it to answer the following questions. Give your answers correct to 3 decimal places. What is the probability a randomly selected student reads exactly 2 of these 3 languages?

The probability that a student reads exactly 2 of these 3 languages is 0.054.

Step-by-step explanation:

Denote the languages as follows:

F = French, G = German and S = Spanish.

The information provided is:

Compute the number of students who study only French and German as follows:

Compute the number of students who study only French and Spanish as follows:

Compute the number of students who study only German and Spanish as follows:

Compute the number of students who reads exactly 2 of these 3 languages as follows:

Thus, there are 27 students who reads exactly 2 of these 3 languages.

Compute the probability that a student reads exactly 2 of these 3 languages as follows:

Thus, the probability that a student reads exactly 2 of these 3 languages is 0.054.

b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation: