Questions: Use complements to find the probability that a card dealt from a full deck (no jokers) is as stated. (Count an ace as high.

Use complements to find the probability that a card dealt from a full deck (no jokers) is as stated. (Count an ace as high.
Transcript text: Use complements to find the probability that a card dealt from a full deck (no jokers) is as stated. (Count an ace as high.
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Solution

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Solution Steps

To find the probability that a card dealt from a full deck is below an ace, we can use the concept of complements. The complement of the event "a card is below an ace" is the event "a card is an ace." We can calculate the probability of drawing an ace and then subtract it from 1 to find the probability of drawing a card below an ace.

  1. Calculate the total number of cards in a deck.
  2. Calculate the number of aces in a deck.
  3. Find the probability of drawing an ace.
  4. Subtract the probability of drawing an ace from 1 to get the probability of drawing a card below an ace.
Step 1: Total Cards in a Deck

A standard deck of cards contains a total of \( 52 \) cards.

Step 2: Number of Aces

In a standard deck, there are \( 4 \) aces.

Step 3: Probability of Drawing an Ace

The probability \( P(A) \) of drawing an ace is calculated as follows: \[ P(A) = \frac{\text{Number of Aces}}{\text{Total Cards}} = \frac{4}{52} = \frac{1}{13} \approx 0.0769 \]

Step 4: Probability of Drawing a Card Below an Ace

The probability \( P(B) \) of drawing a card below an ace is the complement of drawing an ace: \[ P(B) = 1 - P(A) = 1 - \frac{1}{13} = \frac{12}{13} \approx 0.9231 \]

Final Answer

The probability that a card dealt from a full deck is below an ace is approximately \\(\boxed{0.9231}\\).

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