A card is drawn randomly from a standard 52-card deck. Find the following:Write all answers as simplified fractions.Probability the card drawn is a face card.  Probability the card drawn is not a face card.  Odds in favor of drawing a face card.  Odds against drawing a face card.

1. Probability the card drawn is a face card:

A standard deck has 52 cards: 4 suits of 13 cards (Ace through 10, and the face cards Jack, Queen, and King). So there are 3 face cards per suit, and thus 3*4 = 12 face cards in the deck.

The probability of drawing a face card is the number of face cards divided by the total number of cards, or 12/52. This simplifies to 3/13.

2. Probability the card drawn is not a face card:

There are 52 total cards and 12 face cards, so there are 52 - 12 = 40 cards that are not face cards.

The probability of drawing a non-face card is the number of non-face cards divided by the total number of cards, or 40/52. This simplifies to 10/13.

3. Odds in favor of drawing a face card:

Odds in favor are defined as the probability of the event happening divided by the probability of the event not happening.

The probability of drawing a face card is 3/13, and the probability of not drawing a face card is 10/13. So the odds in favor of drawing a face card are (3/13) / (10/13) = 3/10.

4. Odds against drawing a face card:

Odds against are defined as the probability of the event not happening divided by the probability of the event happening.

The probability of not drawing a face card is 10/13, and the probability of drawing a face card is 3/13. So the odds against drawing a face card are (10/13) / (3/13) = 10/3.

1. Probability the card drawn is a face card:

A standard deck has 52 cards: 4 suits of 13 cards each (hearts, diamonds, clubs, spades). Each suit has 3 face cards (King, Queen, Jack). So, there are 4*3 = 12 face cards in a deck.

The probability of drawing a face card is the number of face cards divided by the total number of cards.

So, the probability is 12/52 = 3/13.

2. Probability the card drawn is not a face card:

The number of non-face cards is the total number of cards minus the number of face cards. So, there are 52 - 12 = 40 non-face cards.

The probability of drawing a non-face card is the number of non-face cards divided by the total number of cards.

So, the probability is 40/52 = 10/13.

3. Odds in favor of drawing a face card:

Odds in favor of an event are defined as the probability of the event happening divided by the probability of the event not happening.

So, the odds in favor of drawing a face card are (3/13) / (10/13) = 3/10.

4. Odds against drawing a face card:

Odds against an event are defined as the probability of the event not happening divided by the probability of the event happening.

So, the odds against drawing a face card are (10/13) / (3/13) = 10/3.