In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.

Verified step by step guidance

1. Identify the total number of possible outcomes. Since the card is dealt from a standard deck, there are 52 possible cards.
2. Determine what counts as a 'picture card.' In a standard deck, picture cards are Jacks, Queens, and Kings.
3. Count the number of picture cards in the deck. Each suit (hearts, diamonds, clubs, spades) has one Jack, one Queen, and one King, so multiply 3 picture cards by 4 suits.
4. Set up the probability formula: Probability = (Number of favorable outcomes) / (Total number of possible outcomes).
5. Substitute the values into the formula: Probability = (Number of picture cards) / 52.

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a ratio of favorable outcomes to total possible outcomes. It ranges from 0 (impossible event) to 1 (certain event). In card problems, probability helps determine chances of drawing specific cards.

Sample Space in a Deck of Cards

The sample space is the set of all possible outcomes. For a standard deck, there are 52 unique cards. Understanding the total number of cards is essential to calculate probabilities accurately.

Picture Cards

Picture cards, also called face cards, include Jacks, Queens, and Kings in each suit. Since there are 4 suits, there are 12 picture cards total. Identifying these cards helps determine the number of favorable outcomes.