Finding the probability of a situation. The general formula for finding the probability is the number of events that you’re concerned with over the total number of events in an entire sample space. What we’re looking at here is a class containing 17 girls and 13 guys and considering the probability that the teacher randomly calls on a guy.
For this kind of problem we’re going to assume the teacher is completely unbiased which of course is the case always and what we’re basically going to do is consider the number of outcomes that we want, him calling on a guy over the total number of outcomes, calling on anybody.
Pretty straight forward for this problem there are 13 plus 17, 30 people in this class which he can call on, so that’s going to be our sample space. Calling on each of those students individually, that could be 30 different outcomes. The denominator for our probability is 30. Of those we’re only concerned with the ones that are guys, of which there are 13. He calls on any one of those 13. That’s an even we want so therefore there are 13 events leaving us with the probability of 13/30 that this teacher randomly calls on a guy.