How can the Law of Total Probability find the chance that a randomly selected moviegoer is a minor?

"Suppose that as part of a promotion for Muvico Cinemas movie theatre, we’re planning to give a door prize to the 1000th customer this Saturday afternoon. We want to know the probability that this person will be a minor. Figuring out how many patrons overall will be under 18 might be difficult. But suppose we’re showing three films on Saturday: Spiderman: No Way Home, Here Before, and Sonic the Hedgehog 2. We can estimate the fraction of each movie’s viewers that will be minors: .6, .01, and .95, respectively. We can also predict how many tickets will be sold for each film: 2,000 for Spiderman, 500 for Here Before, and 1,000 for Sonic. Applying frequentist principles, we can compute the probability that a particular visitor will be seeing each of the movies: Pr(Spiderman) = 2000/(2000 + 500 + 1000) = .571, Pr(Here Before) = 500/(2000 + 500 + 1000) = .143, and Pr(Sonic) = 1500/(2000 + 500 + 1000) = .286. The conditional probabilities are Pr(minor | Spiderman) = .6, Pr(minor | Here Before) = .01, and Pr(minor | Sonic) = .95. Now, it’s just a matter of stitching together the parts: Pr(minor) = Pr(minor | Spiderman) Pr(Spiderman) + Pr(minor | Here Before) Pr(Here Before) + Pr(minor | Sonic) Pr(Sonic) = .6 · .571 + .01 · .143 + .95 · .286 = .343 + .00143 + .272 ≈ .616. There are three different ways for a visitor to be a minor: they could be a Spiderman fan and a minor, a Here Before fan and a minor, or a Sonic fan and a minor. Adding up these probabilities is legitimate only because the three movies form a partition of the visitors: every visitor is there to see one and only one movie. The Law of Total Probability comes in handy in scenarios where there’s more than one “way” for an event to occur. It lets you break that event apart into the different ways, then apply your knowledge of the likelihood of each of those ways in order to compute the grand, overall probability of the event."