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

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Identify the total number of possible outcomes. Since you are dealt one card from a standard deck, the total number of outcomes is 52.

Determine what a picture card is. In a standard deck, picture cards are Jacks, Queens, and Kings.

Count the number of picture cards in the deck. There are 4 suits, and each suit has 3 picture cards (Jack, Queen, King), so multiply 4 by 3 to get the total number of picture cards.

Set up the probability formula: Probability = (Number of favorable outcomes) / (Total number of possible outcomes).

Substitute the values into the formula: Probability = (Number of picture cards) / 52.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 how likely it is to draw a specific type of card.

Sample Space

The sample space is the set of all possible outcomes in an experiment. For a standard deck of 52 cards, the sample space includes every individual card. Understanding the sample space is essential to calculate probabilities accurately.

Picture Cards

Picture cards, also called face cards, are the Jack, Queen, and King in each suit. Since there are 4 suits, there are 12 picture cards in total. Identifying the number of favorable outcomes (picture cards) is key to solving the probability question.

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