Answer to Question #329292 in Statistics and Probability for Bfaze

Question

What is the probability that two female students will be selected at random, one after the other, to participate in a research project from a class of 7 male and 3 female students?

Answer 1

The probability of selecting first female is (amount of females / total amount of people) = 3 / 10

After first female is selected, amount of remaining females and total amount of people are decreased by 1, so probability of selecting second female is (3 - 1) / (10 - 1) = 2 / 9.

The resulting probability is equal to production of the previous two:

$P=\frac{3}{10}\cdot\frac{2}{9}=\frac{1}{15}\approx0.0667=6.67\%$