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.

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Alcaa Alcaa · Answer 1 · 2020-02-25T08:35:47+01:00

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) = [tex]\frac{5000}{10000}*\frac{4999}{9999}[/tex] {because we can't select one student twice}

= 0.2499

P(Both students are female) = [tex]\frac{5000}{10000}*\frac{4999}{9999}[/tex] = 0.2499

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

andromache andromache · Answer 2 · 2022-02-15T11:46:46+01:00

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

The Males = 50% of 10,000 = 5000

And, the Females = 50% of 10,000 = 5000

Now

Since two students from this college are selected

So, the probability should be

= male + female

[tex]= (5,000 \div 10,000 \times 4999 \div 9999) + (5,000 \div 10,000 \times 4999 \div 9999)[/tex]

= 0.2499 + 0.2499

= 0.4998

= 0.5

Learn more about the probability here: https://brainly.com/question/10695144