A card is selected from a deck. Find the following probabilities.

A standard deck of cards has 52 Cards. There are 13 values and 4 suits. Suits are Spades, Clubs, Diamonds and Hearts. Each suit has 13 cards. There are 3 face cards Jack, Queen, and King.

a red card = 26/52 = 1/2
a face card = 12/52 = 3/13
a jack and a spade = 4/52 jack, 13/51 spade = 52/2652 = 1/51

Is this correct!

Almost.

red card=26/52=1/2
face card=12/52=3/13
jack and spade=4/52 x 12/51 (Subtracting the jack of spades)=48/2652=4/221

Yes, your analysis is correct.

a red card: There are 26 red cards in the deck (13 hearts + 13 diamonds) out of a total of 52 cards, so the probability of selecting a red card is indeed 26/52, which simplifies to 1/2.

a face card: There are 12 face cards in the deck (4 jacks + 4 queens + 4 kings) out of a total of 52 cards, so the probability of selecting a face card is indeed 12/52, which simplifies to 3/13.

a jack and a spade: There is 1 jack of spades in the deck and 52 cards to choose from initially. After selecting the jack of spades, there are 51 cards remaining in the deck. So, the probability of selecting a jack and a spade is 1/52 * 13/51, which simplifies to 1/51.

Yes, your calculations are correct for the probabilities you have mentioned.

For finding the probability of getting a red card, you correctly identified that there are a total of 52 cards in the deck, out of which 26 are red (13 hearts and 13 diamonds). Therefore, the probability is 26/52, which simplifies to 1/2.

To find the probability of getting a face card, you correctly identified that there are a total of 52 cards in the deck, and among them, there are 12 face cards (4 jacks, 4 queens, and 4 kings). Therefore, the probability is 12/52, which simplifies to 3/13.

For finding the probability of getting a jack and a spade, you correctly identified that there are 4 jacks in the deck, and since there are 52 cards in total, the probability of selecting a jack initially is 4/52. Then, once a jack is already selected, there are 51 cards remaining in the deck, including 13 spades. So the probability of selecting a spade after selecting the jack is 13/51. To find the combined probability, you multiply these individual probabilities: (4/52) * (13/51), which simplifies to 52/2652 or 1/51.

Great job! Your calculations and explanations are correct.