Question

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.

Answer 1

Answer:

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:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3,...$

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

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

$={2\choose 2}(0.50)^{2}(1-0.50)^{2-2}\\=1\times 0.25\times1\\=0.25$

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

Answer 2

Answer:

The probability that they are of the same gender = 0.4998 ≈ 0.5 .

Step-by-step explanation:

We are given that in a certain liberal arts college with about 10,000 students, 50% are males which means;

 Males = 0.5 * 10,000 = 5000                 Females = 0.5 * 10,000 = 5000

Now, two students from this college are selected at random and we have to find the probability that they are of the same gender i.e.;

P(Both students are male)  +  P(both students are female)

P(Both students are male) = $\frac{5000}{10000}*\frac{4999}{9999}$ {because we can't select one student twice}

                                         = 0.2499

P(Both students are female) = $\frac{5000}{10000}*\frac{4999}{9999}$ = 0.2499

Therefore, probability that they are of the same gender = 0.2499 + 0.2499 = 0.4998 ≈ 0.5 .