Interpreting general multiplication rule

we're told that two contestants are finalists in a cooking competition for the final round each of them spin a wheel to determine what star ingredient must be in their dish i guess the primary ingredient and we can see could be charred spinach romaine lettuce i'm guessing cabbage arugula or kale and so then they give us these different types of events or at least the symbols for these different types of events and they give us their meaning so k sub 1 means the first contestant lands on kale k sub 2 means the second contestant lands on kale k sub 1 with this superscript c which you could view is complement so k sub 1 complement the first contest does the first contestant does not land on ko so it's the complement of this one right over here and then k sub 2 complement would be that the second contestant does not land on kl so the the not of k sub 2 right over here using the general multiplication rule express symbolically the probability that neither contestant lands on kale so pause this video and see if you can have a go at this all right so the general multiplication rule is just saying this notion that the probability of two events a and b is going to be equal to the probability of let's say a given b times the probability of b now if they're independent events if the probability of a occurring does not depend in any way on whether b occurred or not then this would simplify to this probability of a given b would just become the probability of a and so if you have two independent events you would just multiply their probabilities so that's just all they're talking about the general multiplication rule but let me express what they are actually asking us to express the probability that neither contestant lands on kale so that means that this is going to happen the first contestant does not land on kale and this is going to happen the second contestant does not land on kl so i could write it this way the probability that k sub 1 complement and k sub 2 complement and i could write it this way this is going to be equal to we know that these are independent events because if the first contestant gets kale or whatever they get it doesn't get taken out of the running for the second contestant the second contestant still has an equal probability of getting or not getting kale regardless of what happened for the first contestant so that means we're just in the situation where we multiply these probabilities so that's going to be the probability of k sub 1 complement times the probability of k sub 2 complement all right now let's do part 2. interpret what each part of this probability statement represents so i encourage you like always pause this video and try to figure that out all right so first let's think about what is going on here so this is this is saying the probability that this is k sub 1 compliment so the first contestant does not land on kale so first first contestant does not get kale and all right and in caps and second contestant does get kale and second does get kale so that's what this left hand is saying and now they say that that is going to be equal to so this part right over here probability that the first contestant does not get kale probability that first does not get kale times right over here and the second part right over here is the probability that the second contestant gets kale given that the first contestant does not get kale so probability that the second gets kale given that's what this vertical line right over here means it means given shorthand for given given i wrote it up there too given that first does not get kale and we're done we've just explained what is going on here