2 students are chosen at random from a group of 120 students that has 60 boys and 60 girls. What is the probability that the students are either both boys or both girls

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

Both boys = 60/120 * 59/119 = ?

Same for both girls.

Either-or probabilities are found by adding the individual probabilities.

To find the probability that the students are either both boys or both girls, we'll first need to calculate the total number of possible outcomes, and then determine the number of favorable outcomes.

Total Number of Possible Outcomes:
From a group of 120 students, we are choosing 2 students at random. This can be represented by the combination formula, nCr, which calculates the number of ways to choose r items from a set of n items without regard for order. In this case, n = 120 (total number of students) and r = 2 (number of students chosen).

Using the combination formula, we have:
nCr = n! / ((n-r)! * r!)
120C2 = 120! / ((120-2)! * 2!)

Now, let's calculate the number of favorable outcomes.

Number of Favorable Outcomes:
For the students to be either both boys or both girls, we have two cases to consider:
1. Both boys: There are 60 boys in the group, and we need to choose 2 of them. So, this can be done in 60C2 ways.
2. Both girls: Similarly, there are 60 girls in the group, and we need to choose 2 of them. This can also be done in 60C2 ways.

Now, we need to find the sum of these two cases to calculate the number of favorable outcomes.

Sum of Cases:
Number of favorable outcomes = 60C2 + 60C2

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = (60C2 + 60C2) / (120C2)

Using a calculator or a software that can calculate combinations, you can plug in these values to find the probability.