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.)
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.)
Solution
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:
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: