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: 4+4=84 + 4 = 8

The total number of cards in the deck is 52. Therefore, the number of cards that are not 5s or 6s is: 528=4452 - 8 = 44

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: Probability=4452\text{Probability} = \frac{44}{52}

Now, simplify the fraction: 4452=1113\frac{44}{52} = \frac{11}{13}

Thus, the probability that Tara does not draw a 5 or 6 is: 1113\boxed{\frac{11}{13}}

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

  1. What is the probability of drawing a 5 or 6 from the deck?
  2. What is the probability of drawing a face card (Jack, Queen, or King)?
  3. What is the probability of drawing a red card (hearts or diamonds)?
  4. What is the probability of drawing an Ace from the deck?
  5. 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