Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are freshmen and two are sophomores. They are put on a wait list. Prior to the start of the semester, two enrolled students drop the course, so the professor randomly selects two of the four wait list students and gives them seats in the class. What is the probability that both students selected are freshmen?

The probability is P = 0.1667 or 16.67%

Step-by-step explanation:

We have 2 slots and 4 possible options.

In the options, we have 2 freshmen and 2 sophomores, and we want to find the probability that the 2 slots are filled with freshmen.

The probability for a freshman to be randomly selected is:

p1 = (number of freshmen)/(number of options) = 2/4 = 1/2

now, for the second selection, we only have 1 freshman and 2 sophomores, so the probability now is:

p2 = 1/3

now, the joint probability of both events happening is equal to the product of the individual probabilities, this is:

P = p1*p2 = (1/3)*(1/2) = 1/6 = 0.1667

if we want the percentage, we must multiply this number by 100%:

P = 0.1667 or 16.67%

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.