Ok so let's consider an example, suppose our random variable X=number of minutes in which the bus arrives and the mean is 20 min. And suppose I have already waited for 23 mins and was wondering whether the bus will arrive within the next minute, so according to me, to calculate that probability I have to look at the area under the curve from 0 to 24 minutes, but that isn't the case. I looked at many videos online but they all had a more mathematical proof rather than a logical one. So what I'm looking for here is a more logical proof rather than a mathematical one. Could someone please help me figure it out?
PS:Please try to use layman terms as far as possible.