Textbook Question
In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.
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10. Combinatorics & Probability
Probability
2:50 minutesProblem 17
Textbook Question
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 guidance1
Start by identifying the total number of possible outcomes. In a standard deck of cards, there are 52 cards.
Next, determine the number of favorable outcomes. There are 4 queens in a standard deck (one for each suit: hearts, diamonds, clubs, and spades).
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Set up the probability formula: \( P(\text{Queen}) = \frac{\text{Number of Queens}}{\text{Total Number of Cards}} \).
Substitute the known values into the formula: \( P(\text{Queen}) = \frac{4}{52} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it quantifies the chance of being dealt a queen from a standard deck of cards. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.
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Favorable Outcomes
Favorable outcomes refer to the specific results that align with the event of interest. In this case, the favorable outcomes are the four queens in a standard 52-card deck. Understanding the number of favorable outcomes is crucial for calculating the probability of drawing a queen.
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Total Outcomes
Total outcomes represent all possible results that can occur in a given scenario. For a standard 52-card deck, the total outcomes when drawing one card is 52. This concept is essential for determining the denominator in the probability calculation, as it provides the context for how many options are available.
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