Questions: If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade?

Solution Steps

To solve this problem, we need to determine the probability of drawing an ace, the king of hearts, or a spade from a standard deck of 52 cards. We will count the number of favorable outcomes and divide by the total number of possible outcomes.

1. Count the number of aces in the deck.
2. Count the number of spades in the deck.
3. Add the king of hearts to the count if it is not already included.
4. Calculate the total number of favorable outcomes.
5. Divide the number of favorable outcomes by the total number of cards in the deck to get the probability.

The total number of cards in a standard deck is: \[ \text{total\_cards} = 52 \]

The number of aces in a deck is: \[ \text{num\_aces} = 4 \]

The number of spades in a deck is: \[ \text{num\_spades} = 13 \]

The king of hearts is a unique card and should be counted separately: \[ \text{king\_of\hearts} = 1 \]

Since one of the aces is a spade, we subtract 1 to avoid double counting: \[ \text{favorable\_outcomes} = \text{num\_aces} + \text{num\_spades} + \text{king\_of\hearts} - 1 \] \[ \text{favorable\_outcomes} = 4 + 13 + 1 - 1 = 17 \]

The probability of drawing an ace, the king of hearts, or a spade is: \[ \text{probability} = \frac{\text{favorable\_outcomes}}{\text{total\_cards}} \] \[ \text{probability} = \frac{17}{52} \]

Final Answer