Question

In a statistics class of students, have volunteered for community service in the past. If two students are selected at random from this class, what is the probability that both of them have volunteered for community service?

Answer 1

Answer:

We do not have the total number of students or volunteers.

I will put variables (and then random numbers) and solve it, then you can put the numbers that you need in the equations.

Suppose that the class has Y students, and X of these students have volunteered.

The probability of picking at random a student that has volunteered is equal to the number of students that had volunteered divided by the total amount of students:

p1 = X/Y

now, we must choose another student, but now the volunteers are X - 1, and the total number of students is also Y - 1 (because we already took one student)

now, the probability of selecting other will be:

p2 = (X- 1)/(Y - 1)

Then, the joint probability of both events is equal to the product of both probabilities:

P = p1*p2 = (X/Y)*((X-1)/(Y -1))

Suppose that there are 20 students, and 10 students that have volunteered, then the equations are:

P = (10/20)*(9/19) = 0.237