Rule of Addition (the OR Rule)

by Jason Amores Sumpter
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So now that we've covered the rule of multiplication in our previous lesson video in this video, we're going to introduce the rule of addition, which is also sometimes referred to as the or role Now. The rule of addition, as its name implies, is going to involve addition. And the rule of addition is also sometimes called the some role or the or role. Now again, we'll explain why it's called the or rule a little bit later here in this video. But the reason it's called the some rules because the sum is the answer to an addition problem. And so the sum is implying addition now, the rule of addition, the some role and the or a role are all referring to the same thing. And really, what they say is that the probability that one independent event or another independent event will occur is calculated by adding their probabilities. And so this is another reason why it's called the or roll. It's because it's involving the probability of one event or another event. And so, for example, the probability that two coins will both land on heads or both land on tails is going to be the probability of one event, plus the probability of another event. So the probability that they both land on heads is 1/4 and the probability that they both land on tails is 1/4 and so the probability that one or the other will occur is 1/4 plus 1/4 and 1/4 plus one. Fourth is, of course, 2/4 and to fourth is the same exact thing as one half. And so there's a 50% chance of two coins landing on heads or two coins landing on tails. And so if we take a look at our image down below, over here on the left hand side, we could get a better understanding of that example with the coins. And again, we know that the first coin flip has a 50% probability of landing on tails, 50% probability of landing on heads and the second coin flip has a 50% probability of landing on heads and a 50% probability of landing on tails since they are independent events. And so if we want the probability that both coins will land on heads, then we need to take the probability of one coin landing on heads and multiply it by the probability of another coin landing on heads and so one half times one half is 1/4. And so the probability that both coins will land on heads is 1/ probability. And the same goes for both coins landing on tails. The probability of one coin landing on tails is one half the probability of another coin landing on tails is one half. And so the probability that both of these coins will land on tails together is one half times one half, which is 1/4. And so the probability that they both will land on heads this 1/4 the probability that they will both land on tales this 1/4. However, to get the probability that the coins will land both on heads or both on tails, we need to take the probability of these occurring independently and add them together. And so the probability of both of them landing on heads is and the probability of both of them landing on tails is one for And so if we want the probability of them landing on heads or landing on tails, then we add them together. And so notice the addition sign here. And 1/4 plus 1/4 is again 2/4 which is the same thing as one half. And so there's a one half probability of them, both of them landing on of them, both landing on heads or both, landing on tails. Now, over here on the right. What we're showing you is another application of the addition role as it applies to this particular example, which says to calculate the probability of having a home mosaic is dominant or a Homo Ziggy's recessive offspring. And so, of course, when we take a look at this pundit square, the probability of getting a Hamas, I guess dominant offspring is 1/ and the probability of getting a Homo zegas recess of offspring is also 1/4 However, to get the probability of getting a Hamas August dominant or a Hamas August recessive, we need toe add these probabilities together, and so the probability that the offspring is home mosaic is dominant is 1/4 the probability that the offspring is Homo zegas process. It is 14 and if we want the probability that one event or the other event will occur. We need to add them. And that's again while we have the addition sign here. And so 1/4 plus 1/4 is to force, which is the same thing as one half. So there's a one half probability, or a 50% probability of the offspring being either Homo Zegas, dominant or homos, I guess. Recessive and with one half here is the answer to this example problem. And so this year concludes our introduction to the rule of addition or the some rule or the aural, and we'll be able to get some practice applying these concepts as we move forward in our course, So I'll see you all in our next video.