# Biostatistics &amp; Epidemiology Lecture Series – Part 2: Probability and Types of Distributions

that’s our denominator and probability of selecting a boys just going to be the number of boys and in that age burg there are a couple of different conditions of probability one is mutual exclusivity so mutually exclusive events the other is conditionally dependent events mutually exclusive means that if one happens the other one is not going to happen so like a coin flip it’s either going to be heads or it’s going to be tails but it can’t be both at the same time role of a single died it’s going to be one of those numbers one through six more germane to that health care the day of week that that a patient arrives you can’t have more than one mechanism of injury mostly although in that if you watch action movies of course the hero can get shot stabbed and cart crash car but usually we classify them as either a fall or a motor vehicle or or motorcycle or assault or something like that gender again mostly is only one so there’s an additive rule among mutually exclusive events and that’s that says that if we want to know the probability that of having one outcome or the other you can just add those probabilities together so in this case we had 4.2 percent of our patients got injured on a motorcycle 15.9% were injured as a motor vehicle occupant that is they were riding in a car or a truck or a van of course there’s no overlap in those so you don’t get any of these yes and yes in here but eighty percent of the of our patients were neither of those so if the assuming those are mutually exclusive the probability of X or Y motorcyclist or motor vehicle occupant is just the probability of X plus probability of Y so if we want to know the proportion of patients that were either motor vehicle occupants or motorcyclists we just add these up 4.2 percent plus 15 point nine percent and get twenty point one percent of our patients fell into one of those categories now conditionally dependent is where the outcome of one variable depends on the other variable or vice versa so like alcohol results in the time of we will see here if your uncalled between midnight and 4:00 am going to see a lot more alcohol patients and if you’re better than if you’re here between 8 a.m. and noon for example survival in GCS of course poor GCS you’ve got poor survival the patient’s gender and the mechanism of injury there’s a little big relationship there so this is looking at the alcohol results alcohol test results by the time of date that the patient arrives and you can see midnight to 359 a.m. nearly 60 percent of our patients tested positive for alcohol going down to 8 to noon that’s it’s more like 10% and you can see how that all shakes out there so there’s a conditional probability going on there with this this is where the we have a multiplicative law so if if those two variables if alcohol and time of day are conditionally probable then the probability of both of those happening together is the probability of X probability of alcohol times the probability of a time of day given alcohol I should probably praise that the other way so the probability of time of day times the probability of alcohol given that time of day so so if we want to know what proportion of patients arrived between midnight and 359 a.m and at A+ alcohol screen then we can look at that the proportion who actually arrived in in that time frame 18 and a half percent and the proportion of those who arrived in that time frame and had a positive alcohol screen 59.2% and if we want to know what proportion of our total patients arrived in that that period of time and had a positive alcohol screen we just multiply these two together to get 11 percent of our patients were patients who arrived between midnight and 359 a.m. and had a positive alcohol screen this will come in handy later it also goes to the concept of Independence when one variable is well testing whether one variable is independent of the other this is an example of something that is not independent so there is a dependence between time of day and alcohol results clearly as as you can see that ranging from from nearly sixty percent all the way down to about 10 percent here so if