The dorm in which you live houses 1% of the total Texas A&M student population.

Question

The dorm in which you live houses 1% of the total Texas A&M student population. You know 30% of the students living in your dorm, but you know only 2% of the rest of Texas A&M student population. A lot of Texas A&M students go to a party (including you) and a host tells you that he will seat you at a table with 3 other people you know. What is the probability that at least one other student at your table is from your dorm? You can assume that the number of people is large, so events of knowing different people at the party are independent.

Explanation / Answer

here probability that you know people from party =0.01*0.30+0.99*0.02=0.0228

therefore probability that the person is from you dorm; given you know him=0.01*0.30/0.0228=0.1316

hence probability that at least one other student at your table is from your dorm =1-P(none is from yur dorm)

             1-(1-0.1316)3 =0.3451

please revert for any clarificaiton required

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