 Hello and welcome to the session. In this session we discuss the following question which says one card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a king of red color, a face card, a red face card, the jack of hearts, a spade, the queen of diamonds. First of all let us see the deck of 52 cards. In this we have four suits namely spades, gloves, hearts and diamonds. Spades and gloves are black in color. These are the black cards and hearts and diamonds are red cards. And each suit has 13 cards that is A, that is A's, then 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q and K. J is the jack, Q is the queen and K is the king. So here as you can see each suit has 13 cards in it and the total becomes 52 cards. So this J is the jack, Q is the queen and K is the king. And these are the face cards. So there are 12 face cards in the deck of 52 cards. This information would help us solving this question. Now we move on to the solution. Now in the question it's given that one card is drawn from a well shuffled deck of 52 cards. So it would mean that the total number of possible outcomes is equal to 52 since we have total 52 cards. And from these 52 cards we draw one card. Now first we need to find the probability of getting a king of red color. So suppose let A be the event of getting a king of red color. So we need to find the probability of A. Now these are the 52 cards. Now consider the kings of red color from these cards shown. Now there would be one king of hearts and one king of diamonds. And we know hearts and diamonds have cards of red color. So this would mean number of kings of red color is equal to 2. One is from the hearts and one is from the diamonds. So now the probability of event A that is probability of getting a king of red color is equal to the number of kings of red color which is 2 upon the total number of possible outcomes which is 52 and 2 26 times is 52. So this is equal to 1 upon 26. That is we get probability of getting a king of red color is equal to 1 upon 26. So the solves are first part of the question. Now let's consider the second part of the question in which we have to find the probability of getting a face card. So we take let B be the event of getting a face card. So we need to find the probability of B. First let's see how many face cards do we have in the collection of 52 cards. These are the 52 cards. Now the face cards are the jacks, the queens and the kings and there are total 12 face cards in the deck of 52 cards. So we write here number of face cards is equal to 12. So now the probability of event B that is probability of getting a face card is equal to number of face cards which is 12 upon the total number of outcomes which is 52. So we get 12 upon 52 is the probability of the event B. Now 4 3 times is 12 and 4 13 times is 52. So this is equal to 3 upon 13 that is you now have probability of the event B that is probability of getting a face card is equal to 3 upon 13. This solves the second part of the question now let's move on to the third part of the question where we have to find out the probability of getting a red face card. So let C be the event of getting a red face card and we need to find the probability of C. You know that the face cards are jacks, queens and the kings that is J, Q and K. But we have to look for the red face cards which means J, Q and K should be red in colour. So we have to look in for the hearts card and the diamonds card. So we find out that there are 3 face cards in the hearts and 3 face cards in the diamonds. That is we have 2 jacks, 2 queens and 2 kings of red colour. So you can say we have 6 red face cards. Thus the number of red face cards is equal to 6. Now the probability of getting a red face card that is probability of C is equal to the number of red face cards which is 6 upon the total number of outcomes that is equal to 52. So probability of C is equal to 6 upon 52. Now 2 3 times is 6 and 2 26 times is 52. So this is equal to 3 upon 26. Thus we say probability of C is equal to 3 upon 26 or probability of getting a red face card is equal to 3 upon 26. This completes the third part of the question. Let's move on to the fourth part of the question where we have to find the probability of getting the jack of hearts. Let D be the event of getting a jack of hearts. So we need to find the probability of D. So total we have 4 jacks that is J, 1 is from space, 1 is from the clubs, 1 is from the hearts and 1 is from the diamonds. And we need to find the probability of getting a jack of hearts. So as you can see we have 1 jack of hearts. So we say the number of jack of hearts is equal to 1. So now probability of the event D that is probability of getting a jack of hearts is equal to number of jack of hearts which is 1 upon the total number of possible outcomes that is 52. So we write here 52. So probability of D is equal to 1 upon 52 that is probability of getting a jack of hearts is equal to 1 upon 52. Next is the fifth part of the question where we need to find the probability of getting a spade. Now consider let E be the event of getting a spade. We need to find the probability of E that is probability of getting a spade. Now as you can see we have 13 cards of spades. So we have the number of spades is equal to 13. So now the probability of the event E that is probability of getting a spade is equal to 13 that is the number of spades upon the total number of possible outcomes which is 52 or the total number of cards. Now 13 4 times is 52 so this is equal to 1 upon 4 that we say probability of event E is equal to 1 upon 4 or probability of getting a spade is equal to 1 upon 4. Now the last part of the question that is the sixth part of the question where we have to find out the probability of getting the queen of diamonds. So let F be the event of getting the queen of diamonds and we need to find the probability of F. So for this first let's see how many queen of diamonds we have. Consider these cards of diamonds as you can see we have just one queen of diamonds. So the number of queen of diamonds is equal to 1. So probability of F that is probability of getting the queen of diamonds is equal to number of queen of diamonds which is 1 upon the total number of cards or the total number of possible outcomes which is 52. So 1 upon 52 is the probability of getting the queen of diamonds that is probability of F. So we have solved all the parts of the given question. So for the first part we get the probability of getting a king of red color is equal to 1 upon 26. The answer for the second part is the probability of getting a face card is equal to 3 upon 13. For the third part we have the probability of getting a red face card is equal to 3 upon 26. Then the fourth part is probability of getting a jack of hearts is equal to 1 upon 52. Then for the fifth part we have the probability of getting a spade is equal to 1 upon 4. And for the sixth part we have the probability of getting the queen of diamonds is equal to 1 upon 52. So our final answer is for the first part it's 1 upon 26. For the second part it's 3 upon 13. For the third part it's 3 upon 26. For the fourth part it's 1 upon 52. For the fifth part it's 1 upon 4. And for the sixth part it's 1 upon 52. So this completes the session. Hope you have understood the solution of this question.