Q5 Finding Complements. In Exercise... [FREE SOLUTION]

Chapter 4: Q5 (page 156)

Finding Complements. In Exercises 5鈥�8, find the indicated complements.
LOL A U.S. Cellular survey of smartphone users showed that 26% of respondents answered 鈥測es鈥� when asked if abbreviations (such as LOL) are annoying when texting. What is the probability of randomly selecting a smartphone user and getting a response other than 鈥測es鈥�?

Expert verified

The probability of selecting a user who has answered other than 鈥測es鈥� is equal to 0.74.

In a survey, 26% of the respondents answered 鈥測es鈥� to a question.

The question inquired, 鈥渋f abbreviations (such as LOL) are annoying when texting.鈥�

If A stands for the occurrence of an event, then denotes the event that A does not occur. In that case, A and arecomplementary events.

Also,

$P (A) + P (\overset{炉}{A}) = 1$

Let A be the event of selecting a user who answered 鈥測es鈥� to the question.

Then, $\overset{炉}{A}$ is the event of selecting a user who did not answer 鈥測es.鈥�

The percentages are divided by 100 to obtain the probability value.

It is calculated as shown below:

$P (\overset{炉}{A}) = 1 - P (A) = 1 - \frac{26}{100} = \frac{74}{100} = 0.74$

Therefore, the probability of selecting a respondent who answered other than 鈥測es鈥� is equal to 0.74.

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