Questions: The table below summarizes results from a study of people who refused to answer survey questions. Use the table to answer the following questions. Be very careful to read the question carefully to determine whether or not there is overlap. 18-21 22-29 30-39 40-49 50-59 60 and over --------------------------------------------------------------- Responded 73 255 245 136 138 202 Refused 12 21 34 27 36 58 If one of the subjects is randomly selected, what is the probability that a randomly selected person is between 22 and 29 years or refused to answer? If one of the subjects is randomly selected, what is the probability that the selected person was between 18 and 21 years or refused to answer?

The table below summarizes results from a study of people who refused to answer survey questions. Use the table to answer the following questions. Be very careful to read the question carefully to determine whether or not there is overlap. 18-21 22-29 30-39 40-49 50-59 60 and over --------------------------------------------------------------- Responded 73 255 245 136 138 202 Refused 12 21 34 27 36 58 If one of the subjects is randomly selected, what is the probability that a randomly selected person is between 22 and 29 years or refused to answer? If one of the subjects is randomly selected, what is the probability that the selected person was between 18 and 21 years or refused to answer?
Transcript text: The table below summarizes results from a study of people who refused to answer survey questions Use the table to answer the following questions. Be very careful to read the question carefully to determine whether or not there is overlap \begin{tabular}{l|cccccc} \multirow{2}{*}{} & \multicolumn{6}{|c}{ Age } \\ \cline { 2 - 7 } & $18-21$ & $22-29$ & $30-39$ & $40-49$ & $50-59$ & 60 and over \\ \hline Responded & 73 & 255 & 245 & 136 & 138 & 202 \\ Refused & 12 & 21 & 34 & 27 & 36 & 58 \end{tabular} If one of the subjects is randomly selected, what is the probability that a randomly selected person is between 22 and 29 years or refused to answer? If one of the subjects is randomly selected, what is the probability that the selected person was between 18 and 21 years or refused to answer?
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Solution

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Solution Steps

Step 1: Sum the counts of the desired outcome across all categories

To find the total number of occurrences of the desired outcome, we sum the counts across all categories: \(\sum D = 188\).

Step 2: Calculate the total count of all outcomes across all categories

The total number of outcomes across all categories is calculated as: \(T = 1237\).

Step 3: Divide the sum of the desired outcome by the total count of outcomes

The probability of the desired outcome is calculated using the formula: \(P(D) = \frac{\sum D}{T} = \frac{188}{1237}\).

Step 4: Round the result as specified

After rounding to 3 decimal places, the probability is: 0.152.

Final Answer:

The probability of the desired outcome, rounded to 3 decimal places, is 0.152.

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