Math Problem Statement
A card is drawn randomly from a standard 52-card deck. Find the following: Write all answers as simplified fractions. Odds against drawing a face card.
Solution
A standard 52-card deck has 12 face cards: 4 Jacks, 4 Queens, and 4 Kings. The total number of cards is 52.
Step 1: Calculate the probability of drawing a face card
The probability of drawing a face card is:
Step 2: Calculate the probability of not drawing a face card
The probability of not drawing a face card is:
Step 3: Calculate the odds against drawing a face card
The odds against drawing a face card is the ratio of the probability of not drawing a face card to the probability of drawing a face card:
So, the odds against drawing a face card are .
Do you want more details or have any questions?
Here are 5 related questions for further practice:
- What are the odds against drawing a King specifically?
- What is the probability of drawing a red card?
- What are the odds in favor of drawing a face card?
- What is the probability of drawing a non-face card?
- How many total black face cards are in the deck?
Tip: When calculating odds, always express them as a ratio between two probabilities—favoring an outcome vs. against that outcome.
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Math Problem Analysis
Mathematical Concepts
Probability
Odds
Formulas
P(Face card) = 12/52 = 3/13
P(Not a face card) = 1 - P(Face card) = 10/13
Odds against drawing a face card = P(Not a face card) / P(Face card) = 10/3
Theorems
Basic probability principles
Odds calculation formula
Suitable Grade Level
Grades 7-9
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