Question

A university conducted a survey of 365 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.

	Freshman	Sophomore	Junior	Senior	Total
Satisfied	54	53	61	55	223
Neutral	24	14	12	13	63
Not satisfied	16	20	14	29	79
Total	94	87	87	97	365

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

Answer 1

a) The probability that he or she is satisfied with student​ government is computed here as:

= Total satisfied / Total

= 223 / 365

= 0.611

Therefore 0.611 is the required probability here.

b) The probability that he or she is a​ junior is computed here as:

= Total Junior / Total

= 87 / 365

= 0.238

Therefore 0.238 is the required probability here.

c) Now the probability that he or she is satisfied and a​ junior is computed here as:

= Total (Junior and satisfied ) / Total

= 61 / 365

= 0.167

Therefore 0.167 is the required probability here.

d) The probability that he or she is satisfied or a​ junior

= Probability that he or she is satisfied + Probability that he or she is junior - Probability that he or she is junior and satisfied

= 0.611 + 0.238 - 0.167

= 0.682

Therefore 0.682 is the required probability here.