Question

A university conducted a survey of

273

​sophomore, junior, and senior undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank.

	Sophomore	Junior	Senior	Total
Satisfied	45

65

63

173

Neutral	16

16

9

41

Not satisfied	17

15

27

59

Total	78

96

99

273

A survey participant is selected at random. What is the probability that he or she is a

junior

AND

neutral

​?

In other​ words, find​ P(person is a

junior

AND

neutral

Answer 1

Let A be the event that the selected participant is junior.

Let B be the event that the selected participant is neutral.

Now to find the probability that the selected participant is junior and neutral , we make use of the conditional probability given by,   

  

To find the probability that the selected person is junior given he is neutral (i.e) P(A|B):

Number of selected participants who are neutral(B) is 41 and the number of juniors(A) among the neutral participants is 16.

Thus the probability that the selected person is junior given he is neutral = 16/41 =0.39

To find the probability that the selected person is neutral (i.e) P(B):

  Number of selected participants who are neutral(B) is 41.

Total number of selected participants is 273.

Thus the probability of selected participant is neutral =41/273=0.15

TO FIND THE PROBABILITY THAT THE PERSON IS JUNIOR AND NEUTRAL:

Since   

  

Thus the P[person is junior and neutral] is 0.059.