Question

a survey of 117 business students at a large university produced the following results. 55 students read business week. 45 students read fortune. 42 students read the wall street journal. 16 students read both business week and fortune. 14 students read both business week and the wall street journal. 9 students read both fortune and the wall street journal. 6 read all three magazines. 8 students read none of these magazines. a) how many students only read fortune? b) how many students just read fortune and the wall street journal? c) how many students read fortune but did not read the wall street journal? check this box to see the answers to the above questions. check this box to see the numbers in the venn diagram. seed = 15

Explanation:

Step1: Define sets and overlaps

Let \( B \) = Business Week, \( F \) = Fortune, \( W \) = Wall Street Journal. All three overlap: \( |B∩F∩W|=6 \).

Step2: Calculate a) Only Fortune

Only \( F \) = Total \( F \) - \( |B∩F| \) - \( |F∩W| \) + \( |B∩F∩W| \)
\( 45 - 16 - 9 + 6 = 26 \)

Step3: Calculate b) Only F & W

Only \( F∩W \) = \( |F∩W| - |B∩F∩W| \)
\( 9 - 6 = 3 \)

Step4: Calculate c) F not W

\( F \) not \( W \) = Only \( F \) + Only \( B∩F \)
Only \( B∩F = |B∩F| - |B∩F∩W| = 16 - 6 = 10 \)
\( 26 + 10 = 36 \)

Answer:

a) 26
b) 3
c) 36