(1 point) For a group of 80 people, assuming that each person is equally likely to...

Question

Question

(1 point) For a group of 80 people, assuming that each person is equally likely to have a birthday on each of 365 days in the year, compute

(a) The expected number of days of the year that are birthdays of exactly 4 people:
E[days with 4 birthdays]=E[days with 4 birthdays]=

(b) The expected number of distinct birthdays:
E[distinct birthdays]=E[distinct birthdays]=

Answer 1

Answer #1

a)probability that 4 people have a birthday on a particular day =⁸⁰C₄(1/365)⁴(364/365)⁷⁶ =0.0000723

hence expected number of days of the year that are birthdays of exactly 4 people =np=365*0.0000723 =0.0264

b)

P(exactly one birthday on a day)=⁸⁰C₁(1/365)¹(364/365)⁷⁹ =0.1764697

hence E[distinct birthdays]= np=365*0.1764697=64.41144

Answer 2

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