One card is selected at random from an ordinary deck of 52. We're going to let a stand for the event. A face card is selected. We're going toe. Let be stand for in the event that a king is selected and we're going toe. Let's see, be the event that a heart is selected. Okay? And with this information, we're going to determine various conditional probabilities. So let's start with part a part. A. Is the probability of event Be so keep in mind there are 52 cards, and probability is always going to be your favorable over your possible. So in this case, there are 52 possible cards, and the favorable is that we select a king and there are four kings in the deck. So the probability of event be would be four out of 52 which simplifies toe 1 13 and as a decimal, that is approximately equal 2.77 part B. The probability of event be given that we know a okay, so we know that we're dealing with a face card. So the face cards are the jacks, the queens and the kings of each suit. So we know there are 12 possible cards because there are 12 face cards. Of those 12 face cards, four of them are kings. We have the king of diamonds, the king of hearts, king of spades and the king of clubs, which simplifies down into one third or approximately equal toe a probability of 0.3 three three. Well, let's go to Part C. What's the probability of be given that we know? See? So this time we know that card is a heart. Well, there happened to be 13 hearts in the deck, and we want a king as the favorable Well, there's only one king of hearts, so therefore, the probability of be given see would be 1/13 which is approximately 0.77 Letter D. What's the probability of be given that not a so not a means? It's not a face card, so not a means that there are 12 less cards in the deck, so there are 40 cards that air not face cards. If they're not face cards, then we'll never get a king. So therefore, the probability of be not a is going to be zero letter E. What is the probability of a well again probability is favorable over possible. There are 52 cards in the deck, and there are 12 face cards as are favorable, and that will reduce down to three out of 13, which, as a decimal, is approximately 0.231 Let her act. What's the probability of a given B? So be Waas that it was a king. So there are four possible kings in the deck. So when we're drawing from those, what's the chances of them having or being a face card? Well, all four would be face cards, so the probability of a given B would be one part G. What's the probability of a given that we know? See, we'll see was a heart, and we know that there were 13 possible hearts of those 13 possible hearts. How many are face cards? Well, there's the jack of hearts, the queen of Hearts and the king of Hearts. So are favorable. Is three making our probability three out of 13, which is approximately point to 31 and the final part to this problem, Part H. What is the probability of a not be well, not be means it's not a face card. Sorry, not being means it's not a king, so that removes four cards from the deck. So we now have 48 possible cards. And if we've removed the four Kings from the deck, we have removed four of the face cards. So there's only eight possible fakes cards leftover that we could access, as are favorable cards, so that simplifies down into 16 which is approximately 0.1 six seven.