Mathematics, 08.12.2020 14:00 pcastaneda03
For a group of 70 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:
Answers: 3
![P = \bigg [ \dfrac{1}{365} \bigg]^4](/tpl/images/0960/5013/eb260.png)
![\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ ^{70}C_{4} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{70-4} \bigg]](/tpl/images/0960/5013/effd9.png)
![\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ \dfrac{70!}{4!(70-4)!} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{66} \bigg]](/tpl/images/0960/5013/5fcfc.png)
![\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ 916895 \times 5.6342 \times 10^{-11} \times 0.8343768898 \bigg]](/tpl/images/0960/5013/d8eab.png)
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