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Carrie and her friends agree that they should each have a party on the day of their 50h birthdays. They agree to invite all of their friends. Assuming the birthdays are spread uniformly across the 52 weeks of the year, how many friends must Carrie invite for there to be a probability greater than one-half of having at least one party in any randomly chosen week? a. 34 b. 35 С. 36 d. 37 e. 38

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Answer #1

let number of people =n

P(at least one party in a week)=1-P(no person have birthday in that week)>1/2

1-(51/52)n >1/2

(51/52)n <1/2

taking log and solving

n >=ln(0.5)/ln(51/52)

n>=35.70

n=36

option C

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