>> The probability of a having a sale at all four offices can be thought of as the probability of a sale and sale and a sale and a sale, and, and using the words and here gives us a tip off that we can multiply probabilities. Now the, so we're talking about the probability of a sale here which is 1/3 and means multiply a probability of the sale of the second goods is 1/3 and then sale of the third visit and sale of the fourth visit. So 1/3 to the 4th power or 1/81 would be the probability of sales at all four of those offices. Now the probability of no sales, it's a very similar idea to this situation, if the probability of making a sale as 1/3 then the probability of not making a sale would be 2/3. So it would be the idea that we have no sale at the first office and no sale at the second office and no sale at the third office and no sale at the fourth office. So it would be 2/3 times 2/3 times 2/3 times 2/3 times 2/3, or 16/81 as that probability. Now here's the one, here's the interesting one in my opinion. The probability of at least one sale, at least one. That's like, that's saying the probability of making one or more sales, now one way to make that calculation is to, to calculate the probability of exactly one sale and add the probability of exactly two and add the probability of exactly three and add the probability of exactly four. You see that's, that's a way to do this, but there's a, there's a better way to do it. Another way is to approach it using the compliment of this business. Now the compliment of this means it, it is not the case that at least one sale occurs, you see if, if, if at least one sale does not occur then that means no sales. So it's 1 minus the compliment of this which is 1 minus the probability of no sales. Now we just calculated the probability of no sales to be 16 x 81, so it's 1 - 16/81 or 65/81, pretty good probability then or that having at least one sale in those four visits. Now by the way this, this compliment idea there is a notation associated with it here and, and I want to show you that notation because you might bump in the problem regarding this, but if, if we're talking about the probability of some event A then the probability of not A is the probability of A prime, that a lot of times is the notation for not A rather than writing the word not, we just put a little prime up here and it means the compliment of A.