A college student is taking 5 courses in a semester. He is willingto assume that

Question

A college student is taking 5 courses in a semester. He is willingto assume that he will get an A
with probability 0.1, a B with probability 0.8, and a C withprobability 0.1 in each of the courses.
He defines X1, X2, X3 to be the number of A’s B’s andC’s respectively that he gets in the semester.
For this multinomial variable situation, find:
a) The probability that the student gets all B’s

b) The probability that the student gets 2 A’s and 3B’s in the semester

c) The probability that he gets no C’s in the semester

Explanation / Answer

5 courses P(a)=.1 P(b)=.8 P(c)=.1 A) all b's= (5!)/{5!)0!(0!)}(.8)5 =.32768 B)2a and3b=5!/[3!(2!)](.8)3(.1)2 =10(.00512)=.0512 c) no c= 1- Probability of all c=1-(5!/5!).15 =.9999

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