Math Problem Statement
Tara randomly draws a card from a standard 52-card deck. What is the probability that she does not draw a 5 or 6? Enter your answer as a fraction, a/b, in simplest form.
Solution
In a standard 52-card deck, there are 4 suits (hearts, diamonds, clubs, spades), and each suit contains one of each rank, including the numbers 5 and 6. Thus, there are:
- 4 cards that are 5s (one for each suit).
- 4 cards that are 6s (one for each suit).
So, the total number of 5s and 6s in the deck is:
The total number of cards in the deck is 52. Therefore, the number of cards that are not 5s or 6s is:
The probability of drawing a card that is not a 5 or 6 is the ratio of the number of favorable outcomes to the total number of outcomes:
Now, simplify the fraction:
Thus, the probability that Tara does not draw a 5 or 6 is:
Would you like further details or have any questions?
Here are 5 related questions for further exploration:
- What is the probability of drawing a 5 or 6 from the deck?
- What is the probability of drawing a face card (Jack, Queen, or King)?
- What is the probability of drawing a red card (hearts or diamonds)?
- What is the probability of drawing an Ace from the deck?
- What is the probability of drawing a card that is either a spade or a 10?
Tip: When simplifying fractions, always check for the greatest common divisor (GCD) to ensure the fraction is in its simplest form.
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Math Problem Analysis
Mathematical Concepts
Probability
Fractions
Formulas
Probability = favorable outcomes / total outcomes
Theorems
Basic Probability Theorem
Suitable Grade Level
Grades 6-8
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