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MUaly pentectly poxiutcly Sken e ner llvely yinnicuic positivcly Ekrted mildly krrud nenuvely Eecle The nber dlsoibutlon Cars Iaid by hen per strictly wrrk symmctic...

Question

MUaly pentectly poxiutcly Sken e ner llvely yinnicuic positivcly Ekrted mildly krrud nenuvely Eecle The nber dlsoibutlon Cars Iaid by hen per strictly wrrk symmctic tollows Toleon posively (1.5) dlstributon TherefOre, the skcwed can be both negarively innctnc skeveu well can poxltively be said anythiog negutively Jbour skewed Supposc shape = jou draw disiribuuon eveni that card at the Card is andomn Red, from probability P(B | Aars and Well-shuffled is the eveht dleck 52 playing cards. Let 113 t

mUaly pentectly poxiutcly Sken e ner llvely yinnicuic positivcly Ekrted mildly krrud nenuvely Eecle The nber dlsoibutlon Cars Iaid by hen per strictly wrrk symmctic tollows Toleon posively (1.5) dlstributon TherefOre, the skcwed can be both negarively innctnc skeveu well can poxltively be said anythiog negutively Jbour skewed Supposc shape = jou draw disiribuuon eveni that card at the Card is andomn Red, from probability P(B | Aars and Well-shuffled is the eveht dleck 52 playing cards. Let 113 that the Card is 1/52 King- 1/4 Then the conditional (d) v2 17. Tlie nuinber of scc (e) None of the Above



Answers

$27-32$ . Conditional Probability These exercises involve conditional probability.
A card is drawn from a deck. Find the following conditional
probability.
(a) The card is a queen, given that it is a face card.
(b) The card is a king, given that it is a spade.
(c) The card is a spade, given that it is a king.

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.

Now I have to find the probability of drawing a king from standard deck of cards, Given that two cards, both kings have already been drawn and not been replaced, two cards have already been drawn, which means in the deck now there are only 50 yards remaining and both of the cars are kings, which means the number of kings present in the deck. Right now, our only two. So what is the probability that I will draw another king? It is going to be two by 15, Or I can write this as one x 25. This is my answer.

Jod a gun beans to the either balls and four valuables and John B. Contains five Red bulls. And to fight bulls, we have to calculate the probability off going do waas In each of the three cases of the force cases probability two balls from jar bees let this be even. Even two balls from Jarvie would be five Cito upon 72. So five picked orifices to withstand upon seven sectorial to sectoral into five Victorian. So this would be band upon 21. No, the second parties probably eat too. Drop one ball from each job. So from jar 80 probably these three c one upon 77 indoor five c one a born again 71 to this would be five steen upon 49 coming to detoured part Probably be off Eat three is what all the balls in Vinger and then brought bulls. A total number of red bulls will be eight So eight c two upon total number of all this 14 14 c two So a factorial upon six pictorial in 2 14 sectorial in 12 Victoria So eight in do seven born 14 and 15 30 14 into 13. So this would be Ford and 777 cancer. This would be four by 14. Now we have to calculate which probably is the largest so 10 upon you and even would give us zero point 47 Atone No. 15 a born 49 would give us at only 0.2. D four by 14. This was before the 39. So this is also around 0.3 of the largest probability is, then we draw two balls from job be.

Now this question says that three cards are drawn from a take without replacement. What is the probability that the three cards are an ace, king and queen in that order? That they are an ace, a king and a queen in that quarter. Okay, So in the deck total there are 52 cards. Now I'm going to draw the first car. Number of cases is four. Alright, so my probability of getting an oasis for by 52, then I proceed to take the next car. Now I want A king. Number of Kings is four, but number of cards left is only 51. Now then I want a queen number of wins again for but the cards left are only 52. Sorry, 15. Right. So this is going to be my answer. This is nothing but four into four into four, Divided by 50, divided by 51, divided by 52. So I answered a 0.000 40 0.00048. This is our answer.


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