1/365 = 0.00274
The probability is approx 0.81
random sample
This is called a random sample.
Simple random sampling.
To determine the probability of 15 random people all having the same birthday, consider each person one at a time. (This is for the non leap-year case.)The probability of any person having any birthday is 365 in 365, or 1.The probability of any other person having that same birthday is 1 in 365, or 0.00274.The probability, then, of 15 random people having the same birthday is the product of these probabilities, or 0.0027414 times 1, or 1.34x10-36.Note: This answer assumes also that the distribution of birthdays for a large group of people in uniformly random over the 365 days of the year. That is probably not actually true. There are several non-random points of conception, some of which are spring, Valentine's day, and Christmas, depending of culture and religion. That makes the point of birth, nine months later, also be non-uniform, so that can skew the results.
The probability is approx 0.81
If you assume that birth dates are uniformly distributed over the year (they are not), and you ignore leap years, then the probability of two people selected at random, share a birthday is 1/365.
The probability is 10 percent.
Birthdays are not uniformly distributed over the year. Also, if you were born on 29 February, for example, the probability would be much smaller. Ignoring these two factors, the probability is 0.0082
It depends on what the random variable is, what its domain is, what its probability distribution function is. The probability that a randomly selected random variable has a value between 40 and 60 is probably quite close to zero.
probability = 2/7 to be exact, 28/97 (about 28.87%)
The probability that 25 random people don't ALL share the same birthday is: 1 - (1/365)**24, or about 0.999999999999999999999999999999999999999999999999999999999999968 However, I suspect you meant to ask "What is the probability that 25 random people all have different birthdays?" That is: 1 * (364/365) * (363/365) * (362/365) * ... * (342/365) * (341/365) = 0.4313 So about 43% of the time nobody will share a birthday, and 57% of the time, two or more people will share a birthday.
random sample
When each member of the population has the same probability of being selected as a member of the sample.
1/7*1/7*1/7*1/7=.0004?
Using the hypergeometric distribution, the answer is 2114/3003 = 0.7040
It is a simple random sample.