Question

in a survey of 800 college students 800, it is found that:274 are majoring in english,156 are majoring in mathematics and422 are majoring in at least one of english and mathematics.A. How many of the 800 are majoring in both english and mathematics?B. how many are majoring in mathematics only?

Answer 1

Answer:

A. There are 17 students that are majoring in both english and mathematics

B. There are 139 students that are majoring in mathematics only

Explanation:

Given that 274 are majoring in english, n(E) = 274

156 are majoring in mathematics, n(M) = 156

422 are majoring in at least one of english and mathematics, n(E U M) = 422

We have:

A. The number of students that are majoring in both english and mathematics is obtained as follows:

$\begin{gathered} n(E\cap M)=n(E)+n(M)-n(E\cup M) \\ \\ =274+165-422 \\ \\ =17 \end{gathered}$

B. The number of students that are majoring in mathematics only is obtained as follows:

$\begin{gathered} n(M\text{ only\rparen=}n(M)-n(M\cap E) \\ \\ =156-17 \\ =139 \end{gathered}$