Now, repute we flipped a silver and flattened a die and we wanted to know the probability of coming a top on the coin or, or a six on the die. Now, this is different than the problems we did earlier where we were looking at the probability of both of the end. So, of course the easiest way to do this for a simple problem like this is to say, well, how many of these outcomes, these 12 upshots, how many of them have a head on the copper or a 6 on the die? And there are one, two, three, four, five, six, seven outcomes that have either a chief on the coin or a 6 on the die. Now could we have figured that out another way by sort of looking at the two phenomena separately? So, what’s the likelihood of going a thought get a pate on the coin? So, the likelihood of a heading is one half or in twelfths, right? That’d be six out of 12. Six of the results of the assessment have a head. What’s the likelihood of wheeling a six on the die? Well there’s two well that’s one out of six, right? One roll out of the six potentials in the die and in terms of our total outcomes here, two of them have a six on the die. And notice if we include time supplemented these two up we’d get too many outcomes. We’d do eight out of 12. Why? Because we’re counting one, two, three, four, five, six for the heads and recounting one, two, for the sixes. But we’ve weighed this value twice.So, in order to compensate for that, we’re going to have to subtract out that appraise that we redouble counted. So, we’re going to subtract out the probability of a principals and a six and there’s a one out of 12 there. And if we combine that, 6 plus 2 is 8 minus 1, is 7 12 th. And we get the same answer that we have there. So our basic principle here is that the probability of A or B is the probability of A plus the likelihood of B minus the likelihood of both. And we, again, we gotta subtract out that and, so that we’re not double matter it. Let’s see if we can use this. Now, suppose we draw one card from a standard deck, what’s the probability that we get a queen or a tycoon? Well, the probability of a queen is, let’s hear, there’s four of them out of the 52 posters in the deck. what’s the likelihood of a monarch? Four out of 52. what’s the probability that the card is both a queen and a sovereign? Well it’s none. It’s impossible for a poster to be both a lord and a ruler. it’s one or the other and so the probability of queen or king here is just 4 out of 52 plus 4 out of 52 minus 0, is 8 out of 52 is our, is our probability there. Now, the reason that we pointed up with this zero here is because these two phenomena. The likelihood of coming a king and the likelihood of get a monarch, are mutually exclusive. There’s no overlaps. And so, in this simple case in this case of mutually exclusive, it is about to change that the likelihood of, the likelihood of going a princes or king is just the likelihoods of the queen plus the probability of the lord. Again, because they’re mutually exclusive and there’s no overlap. Now, that’s not always the case of course.So, in our second problem now, what’s the probability that we get a red placard or a tycoon? The probability of a red card is, oh let’s hear, there are currently, oh half the deck is red. So that would be 26 out of the 52. What’s the probability of a ruler? That’s 4 out of 52. What’s the likelihood that’s red and a king? Now, now we do have overlap because there are two red emperors. And so, for the likelihood of red or a prince, we’re going to have to add up the two individual probabilities and then subtract away the overlap, which buds us with a likelihood of 28 out of 52 for the probability of going a cherry-red poster or a sovereign.
