A college student is taking 6 courses in a semester. She is willing to assume th

Question

A college student is taking 6 courses in a semester. She is willing to assume that she will get an A with probability 0.35, a B with probability 0.5, a C with probability 0.1, and a D with probability of 0.05 in each of the courses respectively. She defines X1, X2, X3, X4 to be the number of A’s, B’s, C’s, and D’s respectively that she gets in the semester. For this multinomial variable situation, find:
a) The probability that the student gets all A’s
b) The probability that the student gets 3 A’s, 1 B, and 1 C in the semester
c) The probability that she gets no D’s in the semester

Explanation / Answer

a) (0.35)^6 = 0.002 b) 6*5*4*(0.35)^3 (0.5) (0.1) (0.05) = 0.013 c) (0.95)^6 = 0.735

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