Questions: A university conducted a survey of 373 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Complete parts (a) through (d) below. (a) If a survey participant is selected at random, what is the probability that he or she is satisfied with student government? P( satisfied )= (Round to three decimal places as needed.) (b) If a survey participant is selected at random, what is the probability that he or she is a junior? P (junior) = (Round to three decimal places as needed.) (c) If a survey participant is selected at random, what is the probability that he or she is satisfied and a junior? P( satisfied and junior )= (Round to three decimal places as needed.) (d) If a survey participant is selected at random, what is the probability that he or she is satisfied or a junior? P( satisfied or junior )= (Round to three decimal places as needed.)

A university conducted a survey of 373 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Complete parts (a) through (d) below.

(a) If a survey participant is selected at random, what is the probability that he or she is satisfied with student government?
P( satisfied )= 
(Round to three decimal places as needed.)
(b) If a survey participant is selected at random, what is the probability that he or she is a junior?

P (junior) = 
(Round to three decimal places as needed.)
(c) If a survey participant is selected at random, what is the probability that he or she is satisfied and a junior?
P( satisfied and junior )= 
(Round to three decimal places as needed.)
(d) If a survey participant is selected at random, what is the probability that he or she is satisfied or a junior?
P( satisfied or junior )= 
(Round to three decimal places as needed.)
Transcript text: A university conducted a survey of 373 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Complete parts (a) through (d) below. (a) If a survey participant is selected at random, what is the probability that he or she is satisfied with student government? $P($ satisfied $)=$ $\square$ (Round to three decimal places as needed.) (b) If a survey participant is selected at random, what is the probability that he or she is a junior? P (junior) $=\square$ $\square$ (Round to three decimal places as needed.) (c) If a survey participant is selected at random, what is the probability that he or she is satisfied and a junior? $P($ satisfied and junior $)=$ $\square$ (Round to three decimal places as needed.) (d) If a survey participant is selected at random, what is the probability that he or she is satisfied or a junior? $\mathrm{P}($ satisfied or junior $)=$ $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

To solve this problem, we need to calculate probabilities based on the given survey data. Here are the steps for each part:

(a) Calculate the probability that a randomly selected participant is satisfied with student government by dividing the number of satisfied participants by the total number of participants.

(b) Calculate the probability that a randomly selected participant is a junior by dividing the number of juniors by the total number of participants.

(c) Calculate the probability that a randomly selected participant is both satisfied and a junior by dividing the number of satisfied juniors by the total number of participants.

(d) Calculate the probability that a randomly selected participant is either satisfied or a junior using the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Step 1: Probability of Satisfaction

To find the probability that a randomly selected participant is satisfied with student government, we use the formula:

\[ P(\text{satisfied}) = \frac{\text{satisfied students}}{\text{total students}} = \frac{210}{373} \approx 0.563 \]

Step 2: Probability of Being a Junior

Next, we calculate the probability that a randomly selected participant is a junior:

\[ P(\text{junior}) = \frac{\text{juniors}}{\text{total students}} = \frac{100}{373} \approx 0.268 \]

Step 3: Probability of Being Satisfied and a Junior

We then find the probability that a randomly selected participant is both satisfied and a junior:

\[ P(\text{satisfied and junior}) = \frac{\text{satisfied juniors}}{\text{total students}} = \frac{50}{373} \approx 0.134 \]

Step 4: Probability of Being Satisfied or a Junior

Finally, we calculate the probability that a randomly selected participant is either satisfied or a junior using the formula for the union of two events:

\[ P(\text{satisfied or junior}) = P(\text{satisfied}) + P(\text{junior}) - P(\text{satisfied and junior}) \] \[ = 0.563 + 0.268 - 0.134 \approx 0.697 \]

Final Answer

\[ \boxed{P(\text{satisfied}) \approx 0.563, \quad P(\text{junior}) \approx 0.268, \quad P(\text{satisfied and junior}) \approx 0.134, \quad P(\text{satisfied or junior}) \approx 0.697} \]

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