 Hello and welcome to the session. Let's walk out the following problem. It says a card is drawn at random from a well-shuffled Deck of 52 cards, find the probability of getting a king, a spade, queen or an ace, a jack, queen or a king, a red card or an ace. Let's now move on to the solution. Now we are given that the total number of cards are 52. In the first part we have to find the probability of getting a king. Now, e is the event of getting a king. The number of king in a deck of 52 cards is 4. So the number of outcomes favorable to e are 4. And we know that the probability of any event e is given by number of outcomes favorable to e, the total number of outcomes. Right. You must remember this formula and write the formula while doing the question. So the probability of getting a king is given by the number of outcomes favorable to e. That is 4 upon the total number of outcomes. And here the total number of outcomes are 52. Since there are 52 cards, so this is equal to 4 by 52, it is equal to 1 upon 13. Now let's further move on to the second part. And here e is the event of getting a spade. So the number of outcomes favorable to e, that is number of spade in a deck of 52 cards is 13. So the probability of getting a spade is equal to the number of outcomes favorable to e upon the total number of outcomes. So the probability is 1 by 4. Now in the c part, this is b and the first one is e. In the c part, we have to find the probability of getting a queen or an ace. So e is the event of getting queen or an ace. Now number of queen is 4 and number of ace is also 4. So the number of outcomes favorable to e, that is ne is the number of queen plus the number of ace. That is 4 plus 4, that is ace 8. So the probability of getting a queen or an ace is equal to 8 by 52, that is the number of outcomes favorable to e upon the total number of outcomes. So this is equal to 2 by 13. Now in the d part, we have to find the probability of getting a jack, queen or a king. So the number of outcomes favorable to e are 4 plus 4 plus 4, that is number of jack plus number of queen plus number of king. So this is equal to 12. So the probability of getting a jack, queen or a king is equal to the number of outcomes favorable to e upon the total number of outcomes. It is 12 by 52 which is equal to 3 by 13. Now in the e part, we have to find the probability of getting a red card. So e is the event of getting a red card. Now the number of outcomes favorable to e are 26 since there are 26 red cards. So the probability of e, that is probability of a red card is equal to the number of outcomes favorable to e upon the total number of outcomes. So the probability is 1 by 2. Now in the f part, we have to find the probability of getting a red ace. Now the number of outcomes favorable to e that is ne are 2 since there are 2 red ace. So the probability of e, that is probability of a red ace will be the number of outcomes favorable to e upon the total number of outcomes. This is equal to 1 by 26. Hence answer to the first part of the question is 1 by 13 to the second part answer is 1 by 4 to the c part answer is 2 by 13 to the d part answer is 3 by 13 to the e part answer is 1 by 2. And to the f part answer is 1 upon 26. 1 by 4 to the c part answer is 2 by 13 to the d part answer is 3 by 13 to the e part answer is 1 by 2. And to the f part answer is 1 upon 26. So this completes the question and the session why we now take care have a good day.