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

Verified step by step guidance

1. Understand the problem: You are asked to find the probability of being dealt a queen from a standard 52-card deck.
2. Recall that a standard deck has 52 cards, and there are 4 queens in the deck (one for each suit: hearts, diamonds, clubs, and spades).
3. Use the probability formula: $P\left(\mathrm{event}\right)=\frac{\mathrm{number\; of\; favorable\; outcomes}}{\mathrm{total\; number\; of\; possible\; outcomes}}$.
4. Substitute the values: the number of favorable outcomes is 4 (queens), and the total number of possible outcomes is 52 (total cards). So, $P\left(\mathrm{queen}\right)=\frac{4}{52}$.
5. Simplify the fraction if possible to express the probability in simplest form.

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 this problem, it helps determine the chance of drawing a queen from the deck.

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 consists of all 52 unique cards. Understanding the sample space is essential to calculate probabilities accurately.

Favorable Outcomes

Favorable outcomes are the specific results that satisfy the event of interest. Here, the favorable outcomes are the four queens in the deck. Counting these correctly is crucial to finding the probability of being dealt a queen.