A card is to be chosen at random from a shuffled deck. Find the probability that the card drawn is

a)the queen of clubs, given that it is an honor card. (I think it is a typo)
b) a red four, given that the face number is even.
c) a seven, given that the face number is prime.

ok, I don't think I answered the questions correctly. I think the answers to all three would be 1/51.

What is an honor card? If an honor card is a face card (J,Q,K), then there are 12 honor (face) cards in a deck.

So a)=1/12
For b) there are 20 numbered cards that are even. There are 2 red fours, So, b)=2/20

To correctly answer the given questions, let's analyze each case individually:

a) The probability of drawing the queen of clubs, given that it is an honor card:

First, let's determine the number of honor cards in a standard deck. In a deck of 52 cards, there are four queens (one of each suit) and three other honor cards (king, jack, and ace) per suit, making a total of 12 honor cards in the deck.

Since we are given that the card is an honor card, there are three possibilities for the card drawn: king, jack, or ace. Only one of those three possibilities is the queen of clubs.

Therefore, the probability of drawing the queen of clubs, given that it is an honor card, is 1/3.

b) The probability of drawing a red four, given that the face number is even:

In a standard 52-card deck, there are four fours (one of each suit). Out of these four cards, two of them are red (hearts and diamonds).

Now, let's determine the number of face cards (cards with face numbers) in the deck. The face numbers are 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. There are 3 face numbers that are even: 2, 4, and 6.

Therefore, out of the two red fours, only one of them has an even face number.

Hence, the probability of drawing a red four, given that the face number is even, is 1/3.

c) The probability of drawing a seven, given that the face number is prime:

Prime face numbers in a standard deck are 2, 3, 5, and 7. Among these prime numbers, only one of them is a seven.

In a deck of 52 cards, there are four sevens (one of each suit). Out of these four cards, only one of them is a prime face number.

Therefore, the probability of drawing a seven, given that the face number is prime, is 1/4.

So, the corrected probabilities are:
a) 1/3
b) 1/3
c) 1/4