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Ymorist [56]
3 years ago
10

For a group of 100 people, compute(a) the expected number of days of the year that are birthdays of exactly 3 people.(b) the exp

ected number of distinct birthdays.
Mathematics
1 answer:
Scilla [17]3 years ago
4 0

Answer:

Step-by-step explanation:

Leaving leap years, a year contains 365 days.

For a group of 100 people, each person is independent of the other and probability of any day being his birthday has a chance of

\frac{1}{365}

a) Probability that  exactly 3 people have same birthday = \frac{1}{365^3}

Each day is independent of the other

And hence no of days having exactly 3 persons birthday out of 100 persons is binomial with n = 365 and p = \frac{1}{365^3}

Expected value of days = np = \frac{1}{365^2}

b) Distinct birthdays is binomail with p =1/365 and n = 365

Hence

expected value = np =1

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