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  • In a class of 200 students, 125 students have take programming language course, 85 students hav taken data structures course, 65 students hav taken computer organization course, 50 student have tak

In a class of 200 students, 125 students have take programming language course, 85 students hav taken data structures course, 65 students hav taken computer organization course, 50 student have taken both programming languages and dat: structures, 35 students have taken both programming languages and compute organization, 30 students have taken both date structures and computer organization, 15 students have taken all the three courses. How many students have not taken any of the three courses?

Option: 1

15


Option: 2

20


Option: 3

25


Option: 4

35


Answers (1)

best_answer

Method I :

         

Using Venn diagram we can easily see that Number of students have not taken any of the three subjects =25

Method II :

\mathrm{Let \; p={programming \; language}, D={Data \; structure}, \& \; \text{C}={computer \; organization}}

Given                 \mathrm{p(P)=\frac{125}{200}, p(D)=\frac{85}{200}, p(C)=\frac{65}{200}}

                          \mathrm{p(P \cap D)=\frac{50}{200}, p(P \cap C)=\frac{35}{200}}

                          \mathrm{p(D \cap C)=\frac{30}{200}, p(P \cap D \cap C)=\frac{15}{200}}

Using Addition theorem, 

                        \begin{aligned} \mathrm{p(P \cup D \cup C)}& = \mathrm{p(P)+p(D)+p(C)-p(P \cap D)}\\ \\- & \mathrm{-p(D \cap C)-p(P \cap C)+p(P \cap D \cap C) }\\ \\& =\frac{7}{8} \end{aligned}

            \begin{aligned} \Rightarrow \mathrm{P}\mathrm{(\overline{\mathrm{P}} \cap \bar{D} \cap \bar{C})} & = \mathrm{1-P(P \cup D \cup C)} \\ \\& =1-\frac{7}{8}=\frac{1}{8} \end{aligned}

Hence, Number of students who had not taken any of the three courses

                                           =\frac{1}{8} \times 200=25

 

Posted by

rishi.raj

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