Questions: Question A magician draws a card out of a standard deck of cards for an illusion. What is the probability that the card is not an ace? Write your answer as a simplified fraction.

$Question A magician draws a card out of a standard deck of cards for an illusion. What is the probability that the card is not an ace? Write your answer as a simplified fraction.$

Transcript text: Question A magician draws a card out of a standard deck of cards for an illusion. What is the probability that the card is not an ace? Write your answer as a simplified fraction.

Solution

Solution Steps

To find the probability that the card drawn is not an ace, we first determine the total number of cards in a standard deck and the number of aces. We then calculate the number of non-ace cards by subtracting the number of aces from the total number of cards. Finally, we divide the number of non-ace cards by the total number of cards to get the probability.

Step 1: Determine Total Cards and Aces

In a standard deck of cards, the total number of cards is given by: \[ \text{Total Cards} = 52 \] The number of aces in the deck is: \[ \text{Aces} = 4 \]

Step 2: Calculate Non-Ace Cards

The number of non-ace cards can be calculated as: \[ \text{Non-Ace Cards} = \text{Total Cards} - \text{Aces} = 52 - 4 = 48 \]

Step 3: Calculate Probability of Not Drawing an Ace

The probability of drawing a non-ace card is given by the ratio of non-ace cards to total cards: \[ P(\text{Not Ace}) = \frac{\text{Non-Ace Cards}}{\text{Total Cards}} = \frac{48}{52} \] This fraction can be simplified: \[ P(\text{Not Ace}) = \frac{12}{13} \]