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You are dealt one card from a 52-card deck. Find the probability that you are not dealt an ace. The probability is ◻ (Type an integer or a fraction. Simplify your answer.)

You are dealt one card from a 5252-card deck. Find the probability that you are not dealt an ace.\newlineThe probability is □ \square (Type an integer or a fraction. Simplify your answer.)

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Full solution

Q. You are dealt one card from a 5252-card deck. Find the probability that you are not dealt an ace.\newlineThe probability is □ \square (Type an integer or a fraction. Simplify your answer.)
  1. Count Aces: Determine the total number of aces in a standard 5252-card deck.\newlineThere are 44 aces in a deck (one for each suit: hearts, diamonds, clubs, and spades).
  2. Calculate Non-Aces: Calculate the number of cards that are not aces.\newlineSince there are 5252 cards in total and 44 of them are aces, the number of cards that are not aces is 52−452 - 4.\newline52−4=4852 - 4 = 48
  3. Calculate Probability: Calculate the probability of not being dealt an ace.\newlineThe probability is the number of favorable outcomes (not getting an ace) divided by the total number of possible outcomes (any card from the deck).\newlineProbability = Number of cards that are not aces / Total number of cards\newlineProbability = 4852\frac{48}{52}
  4. Simplify Fraction: Simplify the fraction to express the probability in simplest terms. \newline4852\frac{48}{52} can be simplified by dividing both the numerator and the denominator by 44.\newline48÷4=1248 \div 4 = 12\newline52÷4=1352 \div 4 = 13\newlineSo, the simplified fraction is 1213\frac{12}{13}.

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