Questions: 1) What is the probability of selecting the king of hearts?

1) What is the probability of selecting the king of hearts?

Solution

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Solution Steps

To find the probability of selecting the king of hearts from a standard deck of 52 cards, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. There is only one king of hearts in a deck of 52 cards.

Step 1: Determine the Total Number of Cards

A standard deck of cards contains 52 cards. Therefore, the total number of possible outcomes is: \[ \text{Total cards} = 52 \]

Step 2: Determine the Number of Favorable Outcomes

There is only one king of hearts in a standard deck of cards. Therefore, the number of favorable outcomes is: \[ \text{Favorable outcomes} = 1 \]

Step 3: Calculate the Probability

The probability \( P \) of selecting the king of hearts is given by the ratio of the number of favorable outcomes to the total number of possible outcomes: \[ P = \frac{\text{Favorable outcomes}}{\text{Total cards}} = \frac{1}{52} \]

Step 4: Simplify the Probability

Simplifying the fraction and converting it to a decimal: \[ P = \frac{1}{52} \approx 0.0192 \]

Final Answer

\(\boxed{P = \frac{1}{52}}\)

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