Question

the venn diagram below shows the results of a survey of 200 readers on the type of magazine they read. if a respondent is chosen at random, what is the probability that the respondent reads a technology or a business magazine? a. 11/20 b. 9/20 c. 11/20 d. 1/2

Explanation:

Step1: Find number of readers who read tech or business

Use the formula for the union of two - sets in a Venn - diagram. The number of readers who read a technology or a business magazine is the sum of the number of readers who read only technology, only business, and both. So, \(n(\text{Tech}\cup\text{Bus})=60 + 10+50=120\).

Step2: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the total number of respondents is \(N = 200\), and the number of favorable outcomes (readers who read a technology or a business magazine) is \(n = 120\). So, \(P=\frac{120}{200}=\frac{3}{5}\).

Answer:

None of the given options (A. \(\frac{11}{20}\), B. \(\frac{9}{20}\), C. \(\frac{11}{20}\), D. \(\frac{1}{2}\)) are correct. The correct probability is \(\frac{3}{5}\).