If two students are randomly selected without replacement, find the probability

Question

If two students are randomly selected without replacement, find the probability that they both have green eyes. A class is collecting data on eye color and gender. They organize the data they collected into the table shown. Numbers in the table represent the number of students from the class that belong to each of the categories. Use the data to find the probability th selected student from this class belong to each of the categories. Use the data to find the probabity that a randomly Brown Blue Green 18 10 22 1 50 Female | 18 | 20 | 12- 2 Male loo

Explanation / Answer

There are total 100 students out of which 22 has green eyes. So the probability that first student has green eyes is

P(frist student has green eyes) = 22/100

And after selecting first student, number of remaining students is 99 out of which 21 has green eyes so

P(second student has green eyes | frist student has green eyes) = 21/99

So the probability that they both have green eyes is

P(second student has green eyes and frist student has green eyes)= P(second student has green eyes | frist student has green eyes) P(frist student has green eyes)=(22/100)*(21/99) = 0.0467

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