Let's go through each question using the information in the image.

Solution:

1. Total Cards: A standard deck has 52 cards.

(a) What is the probability that the card drawn is a heart?

• There are 13 hearts in the deck (one for each rank: Ace, 2, 3, ..., King).
• Probability $P(\text{Heart}) = \frac{\text{Number of Hearts}}{\text{Total Cards}} = \frac{13}{52} = \frac{1}{4}$.

Answer for (a): $\frac{1}{4}$.

(b) What is the probability that the card drawn is a four?

• There are 4 fours in the deck (one in each suit: Hearts, Diamonds, Spades, Clubs).
• Probability $P(\text{Four}) = \frac{\text{Number of Fours}}{\text{Total Cards}} = \frac{4}{52} = \frac{1}{13}$.

Answer for (b): $\frac{1}{13}$.

(c) What is the probability that the card drawn is a heart and a four?

• There is only one card that is both a heart and a four (the Four of Hearts).
• Probability $P(\text{Heart and Four}) = \frac{\text{Number of Fours of Hearts}}{\text{Total Cards}} = \frac{1}{52}$.

Answer for (c): $\frac{1}{52}$.

Would you like any further details or explanations on these solutions?

Related Questions:

1. What is the probability of drawing a red card from a standard deck?
2. What is the probability of drawing a face card (Jack, Queen, or King)?
3. What is the probability of drawing a black card that is a spade?
4. What is the probability of drawing an Ace?
5. What is the probability of drawing a card that is either a heart or a four?

Tip:

In probability, if you want to find the probability of drawing either of two types of cards, you can add their individual probabilities only if there’s no overlap between the two categories.