Answer to Question #140406 in Statistics and Probability for Ojugbele Daniel

Question

Two questions A and B were given to 50 students as class work. 23 of them could answer question A but not B. 15 of them could answer B but not A. If 2x of them could answer none of the two questions and 2 could answer both questions.

Represent the information in a Venn diagram. (b) Find the value of x

Answer 1

According to question ,

$|A-B|=23 ,|B-A|=15,|A\cap B|=2$ and $|(A\cup B)^c|=2x$

Let $\varOmega=$ Total number of student.

Therefore $|\varOmega|=50$

Which is represented by venndiagram as follow

We know that from basic set theory ,

$|A\cup B|=|A|+|B|-|A\cap B|$

$\implies |A\cup B|=23+15-2=36$

Now $|(A\cup B)^c| =$ $|\varOmega|-|A\cup B|=50-36=14$

$\implies 2x=14$

$\implies x=7$