A small university has a total enrollment of 1600 students. Out of this total, G

Question

A small university has a total enrollment of 1600 students. Out of this total, Graduate students are 600.   Out of the total university enrollment Full Time students are 900, and 200 are Graduate students who are Full Time. Consider the following events for students:

FT=”Full Time”, PT=”Part Time”, UN=”Undergraduate”, GR=”Graduate”.

Calculate the following probabilities:

P(FT); P(PT); P(UN); P(GR);

P(PT&UN); P(FT&GR); P(UN&GR);

P(PT or UN); P(FT or UN); P(PT or FT);

P( not UN); P(FT or notGR);

P(FTGR); P(UNPT);

Are FT and GR mutually exclusive?   Why ?

Are FT and GR independent ? Why ?

Are UN and GR mutually exclusive ? Why ?

Are UN and GR independent ? Why ?

* no handwriting

Explanation / Answer

n(S) = 1600

n(GR) = 600
P(GR) = 600/1600 = 3/8

n(FT) = 900
P(FT) = 900/1600 = 9/16

n(UN) = 1600 - 600 = 1000
P(UN) = 1000/1600 = 5/8

n(PT) = 1600 - 900 = 700
P(PT) = 700/1600 = 7/16

n(FT & GR) = 200
P(FT & GR) = 200/1600 = 1/8

n(FT or GR) = n(FT) + n(GR) - n(FT & GR)
n(FT or GR) = 900 + 600 - 200 = 1300
P(FT or GR) = 1300/1600 = 13/16

n(PT & UN) = 1600 - 700 - 400 - 200 = 300
P(PT & UN) = 300/1600 = 3/16

n(PT or UN) = n(PT) + n(UN) - n(PT & UN)
n(PT or UN) = 700 + 1000 - 300 = 1400
P(PT or UN) = 1400/1600 = 7/8

n(UN & GR) = 0 (As both are mutually exclusive)
P(UN & GR) = 0

n(FT & UN) = 900 - 200 = 700
n(FT or UN) = n(FT) + n(UN) - n(FT & UN)
n(FT or UN) = 900 + 1000 - 700 = 1200
P(FT or UN) = 1200/1600 = 12/16

n(PT or FT) = 1600 (as events are mutually exclusive)
P(PT or FT) = 1

P(not UN) = 1 - P(UN) = 1 - 5/8 = 3/8

P(FT or not GR) = 700/1600 = 7/16

P(FT|GR) = P(FT & GR)/P(GR) = 1/3

P(UN|PT) = P(UN & PT)/P(PT) = 3/7

FT and GR are not mutually exclusive because P(FT) + P(GR) not equals to 1
FT and GR are not independent because P(FT)*P(GR) not equals to P(FT & GR)

UN and GR are mutually exclusive because P(FT) + P(GR) equals to 1
UN and GR are not independent because P(UN)*P(GR) not equals to P(UN & GR)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.