Question

Suppose a student must take an oral exam on three of ten possible topics.She has studied eight of these topics, but did not have time to study the final twotopics. On the day of the exam, she must randomly select three of ten cards (onefor each possible topic) and answer questions on those three topics. Determinethe probability that she will be examined on 0, 1, 2, or 3 topics that she hasstudied for (i.e., compute the four specified probabilities). Explain.

Answer 1

here X are number of topics from 8 which she has studied

probability that she will be examined on 0  topics that she has studied =P(X=0)=P(selecting 0 from 8 and 3 from remaining 2) =0 (since there are only 2 topics which she has not studied, it is not possible to have 3 topics not studied from cards

P(X=1) =P(select 1 from 8 studied and 2 from 2 not studied) =(8C1)*(2C2)/(10C3)=8*1/120=1/15

P(X=2)=P(select 2 from 8 studied and 1 from 2 not studied) =(8C2)*(2C1)/(10C3)=28*2/120=7/15

P(X=3)=P(select 3 from 8 studied and 0 from 2 not studied) =(8C3)*(2C0)/(10C3)=56*1/120=7/15