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probability question

I wrote a story where 70 children are at camp for three weeks. I want only one girl to have a birthday during that time, but my editor thinks that's unlikely and wants me to change it. Can anyone help me with some percentages or probability in my favor? Thanks so much!

Respuesta :

Answer:

23 kids can have a birthday during the three weeks. Hope this answer helps.

Step-by-step explanation:

OK, so there are 70 kids, divide 70 by 3. Than that can be your answer.

MathPhys

Step-by-step explanation:

Three weeks is 21 days.  There are 365 days in a year.  So the probability that a person's birthday is in those three weeks is 21/365.

The probability that exactly 1 person out of 70 has a birthday in that time can be found with binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

P = ₇₀C₁ (21/365)¹ (1 − 21/365)⁷⁰⁻¹

P = 70 (21/365) (344/365)⁶⁹

P ≈ 0.0675

There is a 6.75% probability that exactly one of the 70 children has a birthday during those three weeks.

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