Question

Let

X equal the number of people selected at random that you must ask in order to find someone with the same birthday as yours. Assume that each day of the year is equally likely, and ignore February 29.
What is the probability distribution for
X in this scenario?
a) Uniform distribution
b) Normal distribution
c) Exponential distribution
d) Binomial distribution

Answer 1

The probability distribution for X in this scenario is the Geometric distribution.

Step-by-step explanation:

The probability distribution for X in this scenario is the Geometric distribution.

In the Geometric distribution, the random variable X represents the number of trials it takes to achieve the first success. In this case, the success is finding someone with the same birthday as yours.

Each day of the year is equally likely, so the probability of finding a match on any given trial is 1/365. The probability of finding a match on the first trial is 1/365, the second trial is (364/365) * (1/365), the third trial is (364/365) * (363/365) * (1/365), and so on.