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Chapter 11: Problem 1

In Exercises 1-6, you are dealt one card from a 52-card deck. Find the probability that you are not dealt an ace.

Short Answer

Expert verified
The probability of not being dealt an ace from a 52-card deck is \( \frac{12}{13} \)

Step by step solution

01

Define the total number of outcomes

In any deck of 52 playing cards, the total number of outcomes when drawing a card is 52 since there are 52 cards in a deck.
02

Define the number of favorable outcomes

In any deck of 52 cards, there are 4 aces. So, the favorable outcomes when drawing an ace is 4.
03

Calculate the number of outcomes for the complementary event

We are interested in the complementary event (not drawing an ace), so the number of outcomes for this is the total number of outcomes (52) minus the number of outcomes that are an ace (4). This results in \(52 - 4 = 48\).
04

Calculate the probability of not getting an ace

The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability of not getting an ace can be calculated as the ratio of the number of outcomes that are not an ace (48) to the total number of outcomes (52), which in fraction form is \( \frac{48}{52} = \frac{12}{13} \)

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