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NemiM [27]
3 years ago
12

A company with n employees publishes an internal calendar, where each day lists the employees having a birthday that day. What i

s the probability there is at least one day in a year when nobody has a birthday?
Mathematics
1 answer:
lutik1710 [3]3 years ago
5 0

Answer: 1-(\frac{364}{365})^n

Step-by-step explanation:

Binomial probability formula :-

P(x)=^nC_xp^x(1-p)^x, where P(x) is the probability of getting success in x trials, n is the total number of trials and p is the probability of getting success in each trial.

We assume that the total number of days in a particular year are 365.

Then , the probability for each employee to have birthday on a certain day :

p=\dfrac{1}{365}

Given : The number of employee in the company = n

Then, the probability there is at least one day in a year when nobody has a birthday is given by :-

P(x\geq1)=1-P(x

Hence, the probability there is at least one day in a year when nobody has a birthday =1-(\frac{364}{365})^n

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