Questions: What is the probability of getting either a spade or a king when drawing a single card from a deck of 52 cards? What is the probability that the card is either a spade or a king? (Simplify your answer. Type an integer or a fraction.)

What is the probability of getting either a spade or a king when drawing a single card from a deck of 52 cards? What is the probability that the card is either a spade or a king? (Simplify your answer. Type an integer or a fraction.)
Transcript text: Question 9 of 19 This question: 1 point(s) possible Submit test What is the probability of getting either a spade or a king when drawing a single card from a deck of 52 cards? What is the probability that the card is either a spade or a king? $\square$ (Simplify your answer. Type an integer or a fraction.)
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Solution

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Solution Steps

To solve this problem, we need to calculate the probability of drawing either a spade or a king from a standard deck of 52 cards.

  1. Calculate the number of spades in the deck.
  2. Calculate the number of kings in the deck.
  3. Subtract the overlap (the king of spades) since it is counted twice.
  4. Divide the total number of favorable outcomes by the total number of possible outcomes (52 cards).
Step 1: Total Cards in a Deck

A standard deck of cards contains a total of \( 52 \) cards.

Step 2: Count of Spades and Kings

In the deck, there are \( 13 \) spades and \( 4 \) kings. However, one of the kings is also a spade (the king of spades), which we need to account for.

Step 3: Calculate Favorable Outcomes

To find the total number of favorable outcomes for drawing either a spade or a king, we use the formula: \[ \text{Favorable Outcomes} = \text{Spades} + \text{Kings} - \text{Overlap} \] Substituting the values: \[ \text{Favorable Outcomes} = 13 + 4 - 1 = 16 \]

Step 4: Calculate Probability

The probability \( P \) of drawing either a spade or a king is given by: \[ P = \frac{\text{Favorable Outcomes}}{\text{Total Cards}} = \frac{16}{52} \] This simplifies to: \[ P = \frac{4}{13} \approx 0.3077 \]

Final Answer

The probability of drawing either a spade or a king is approximately \( 0.3077 \) or in fractional form \( \frac{4}{13} \). Thus, the final answer is: \[ \boxed{\frac{4}{13}} \]

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