A random sample of 250 juniors majoring in psychology or communication at a large university is selected. These students are asked whether or not they are happy with their majors. Assume that none of these 250 students is majoring in both areas. There are a total of 100 majoring in psychology and only 80 of those majoring in psychology are happy while 35 students majoring in communication are unhappy.
If one student is selected at random from this group, find the probability that this student is:________
i. happy with the choice of major
ii. a psychology major
iii. a communication major given that the student is happy with the choice of major
iv. unhappy with the choice of major given that

Solution :

It is given that :

Number of students in a random sample majoring in communication or psychology at an university = 250

Total number of students majoring in psychology = 100

Number of students majoring in psychology  those who are happy = 80

So number of students majoring in psychology  those who are not happy = 20

Total number of students majoring in communication = 250 - 100 = 150

Number of students majoring in communication  those who are happy = 115

So number of students majoring in psychology  those who are not happy = 35

a). Probability of the students happy with their major choices are

    [tex]$=\frac{80+115}{250}$[/tex]

    = 0.78

b). Psychology major [tex]$=\frac{80+20}{250}$[/tex]

                                   = 0.4

c). Probability of the students who are happy with the communication as the choice of major = [tex]$\frac{115}{250}$[/tex] = 0.46

d). Students unhappy with their choice of major given that the student is psychology major = [tex]$\frac{20}{250}$[/tex]  =  0.018

a) Probability of the students happy with their major choices is 0.78.

b) Probability of Psychology major is 0.4

c) Probability of the students who are happy with the communication as the choice of major is 0.46.

d) Students unhappy with their choice of major given that the student is psychology major is 0.018

Given:

Number of students in a random sample majoring in communication or psychology at an university = 250

Total number of students majoring in psychology = 100

Number of students majoring in psychology  those who are happy = 80

So, number of students majoring in psychology those who are not happy = 20

Total number of students majoring in communication = 250 - 100 = 150

Number of students majoring in communication  those who are happy = 115

So, number of students majoring in psychology  those who are not happy = 35

a). Probability of the students happy with their major choices are

[tex]=\frac{80+115}{250} =0.78[/tex]

b). Psychology major

[tex]\frac{80+20}{250} =0.4[/tex]

c). Probability of the students who are happy with the communication as the choice of major =[tex]\frac{115}{250} =0.46[/tex]

d). Students unhappy with their choice of major given that the student is psychology major =[tex]\frac{20}{250} =0.018[/tex]

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