In a certain liberal arts college with about 10,000 students, 50% are males. If two students from this college are selected at random, what is the probability that they are of the same gender? Your answer should be rounded to 4 decimal places.

The probability that both the students selected are of the same gender is 0.25.

Step-by-step explanation:

Let X = number of students selected of the same gender.

The probability of selecting a student of a particular gender is,

P (X) = p = 0.50.

The number of students selected is, n = 2.

The random variable follows a Binomial distribution.

The probability of a binomial distribution is computed using the formula:

Compute the probability that both the students selected are of the same gender as follows:

P (Both boys) = P (Both girls) = P (X = 2)

Thus, the probability that both the students selected are of the same gender is 0.25.

step-by-step explanation:

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