Questions: A university conducted a survey of 389 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Freshman Sophomore Junior Senior Total --------------- Satisfied 57 52 65 59 233 Neutral 30 15 13 14 72 Not satisfied 19 18 19 28 84 Total 106 85 97 101 389 If a survey participant is selected at random, what is the probability that he or she is satisfied and a junior?

A university conducted a survey of 389 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Freshman Sophomore Junior Senior Total --------------- Satisfied 57 52 65 59 233 Neutral 30 15 13 14 72 Not satisfied 19 18 19 28 84 Total 106 85 97 101 389 If a survey participant is selected at random, what is the probability that he or she is satisfied and a junior?
Transcript text: A university conducted a survey of 389 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. \begin{tabular}{lcccccc} & Freshman & Sophomore & Junior & Senior & Total \\ \hline Satisfied & 57 & 52 & 65 & 59 & 233 \\ \hline Neutral & 30 & 15 & 13 & 14 & 72 \\ \hline Not satisfied & 19 & 18 & 19 & 28 & 84 \\ \hline Total & 106 & 85 & 97 & 101 & 389 \\ \hline \end{tabular} If a survey participant is selected at random, what is the probability that he or she is satisfied and a junior?
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Solution

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Solution Steps

Step 1: Identify the Relevant Values

From the survey data, we know that the total number of undergraduate students surveyed is \( 389 \) and the number of juniors who are satisfied is \( 65 \).

Step 2: Set Up the Probability Formula

The probability \( P \) that a randomly selected participant is both satisfied and a junior can be expressed as: \[ P(\text{satisfied and junior}) = \frac{\text{Number of satisfied juniors}}{\text{Total number of students}} = \frac{65}{389} \]

Step 3: Calculate the Probability

Now, we compute the probability: \[ P(\text{satisfied and junior}) = \frac{65}{389} \approx 0.167 \] Rounding to three decimal places, we find: \[ P(\text{satisfied and junior}) \approx 0.167 \]

Final Answer

\(\boxed{0.167}\)

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