Question

A survey is made of sources of news for people. It is of interest whether people obtain their news from television (Event T), a newspaper (Event N), or social media (Event S). Suppose that 77% people obtain news from television, 63% from newspapers, 47% from social media, 45% from television and newspapers, 29% from television and social media, 21% from newspapers and social media, and 6% from television, newspapers, and social media.

Question: Find the proportion who do not obtain news from any of these three sources.

Answer 1

Given T = 77, N = 63, S = 47, T&N = 45, T&S = 29, N&S = 21, T&N&S = 6. The Popopulation = 100

Thereare 2 ways to do this

(1) According to set theory: = T + N + S - (T&N) - (T&S) - (N&S) + (T&N&S) + Neither 3

Therefore - {T + N + S - (T&N) - (T&S) - (N&S) + (T&N&S)} = Neither 3

Neither 3 = 100 - (77 + 63 + 47 - 45 - 29 - 21 + 6) = 100 - 98 = 2%

(2) This is by the method of Venn Diagrams. The same is attached below.