Answer to Question #347774 in Discrete Mathematics for bel

Question

In a survey of 120 professors, a research found that 50 preferred traditional method of teaching, 78

preferred computer-aided method, and 66 preferred group method. In addition, 36 preferred any of

the two methods of teaching and 24 professors preferred them all.

a. Find the number of professors who prefer at least one of the teaching methodologies

b. Find the number of professors who do not prefer any of the teaching methodology

Answer 1

a.

$$P(T\cup C\cup G)=P(T)+P(C)+P(G)$$

$$-P(T\cap C)-P(T\cap G)-P(C\cap G)$$

$$+P(T\cap C\cap G)$$

$$=\dfrac{50}{120}+\dfrac{78}{120}+\dfrac{66}{120}-\dfrac{36}{120}-\dfrac{36}{120}-\dfrac{36}{120}+\dfrac{24}{120}$$

$$=\dfrac{11}{12}$$

b.

$$P(\overline{T\cup C\cup G})=1-P(T\cup C\cup G)$$

$$=1-\dfrac{11}{12}=\dfrac{1}{12}$$