Probability | Worked example

- [Instructor] We have a probability question here and it says of the 30 students in Mr. McDaniel's music theory class, 10 do not play any instruments, 14 play only one instrument, and the rest play two or more instruments. If one student is selected at random, what is the probability that the student plays two or more instruments? So pause this video and see if you can figure this out on your own before we work through it together. Okay, now what are we trying to figure out? We wanna figure out the probability that a given student, a random student, plays two or more instruments. So random, randomly selected student. I'll write it in. Student. Student plays two or more more instruments. So when you're doing a probability question like this we know what our denominator's gonna be. It's gonna be, well, how many students are we picking from? Well, we're picking from 30 students. We are picking from 30 students. And then how many of those 30 students meet this condition that they play two or more instruments? Well, it says here 10 do not play any instruments, 14 play only one instrument, and the rest play two or more instruments. So how many is in that rest group? Well, let's see. 10 here, 14 here, so that makes up 24. So 24 play one or less instrument. And so the rest is what we need to get to 30. So that would be six. So one way to think about it, 10 plus 14 plus the rest, I'll put that in quotes, needs to be equal to 30. And so all I said, okay. This is no instruments, this is one instrument, so that's 24 play one or fewer instruments plus the rest that they talk about. And these are who we are interested in. These are the people who play two or more instruments is equal to 30. And so we know that six students play two or more instruments. They could have said and six play two or more instruments, but they wanted us to figure that out. So the probability of a random student playing two or more instruments, well it's the number of students who meet that constraint, six, over the number of possible students. So 6/30. Well, when you look at the choices, you don't see 6/30, but that's because we can rewrite this fraction. Let's see, six and 30 are both divisible by six. And so if you divide the numerator by six, you get one. And you divide the denominator by six, you get five. So anything you do to the numerator of a fraction, as long as you do it to the denominator as well, it doesn't change the value of the fraction. So we just divided the numerator and the denominator by six to get to 1/5. And we do see that choice right over there.