Question
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If you draw a random card from a standard deck of 52 cards, what are the odds of drawing the jack, queen, king, or ace of diamonds? Write your answer in the form \( a: b \) as a fully reduced ratio. Note: In a standard deck of cards, each of the four suites has three face cards and one ace.

Ask by Williams Mccarthy. in the United States
Feb 25,2025

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Tutor-Verified Answer

Answer

The odds are 1:12.

Solution

There are 4 favorable cards (the jack, queen, king, and ace of diamonds) out of a total of 52 cards. This means there are 52 - 4 = 48 unfavorable outcomes. The odds in favor are expressed as the ratio of favorable outcomes to unfavorable outcomes: Odds = 4:48, which reduces to 1:12. Thus, the odds of drawing a jack, queen, king, or ace of diamonds are 1:12.

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The Deep Dive

In a standard deck of 52 cards, there are four specific cards you want to draw: the jack, queen, king, and ace of diamonds. This gives you a total of 4 favorable outcomes. The total number of cards is 52, so the odds are calculated as 4 favorable outcomes to 48 unfavorable outcomes. This simplifies to \( 1: 12 \). When it comes to card games or probability puzzles, knowing the odds can help you make strategic decisions. For example, if you're playing poker, understanding the likelihood of drawing specific cards can influence your betting. The more you grasp about odds, the cooler and more calculated your game can become! Card games have been a staple of entertainment for centuries! They originated over a millennium ago in China, making their way to Europe by the 14th century. The designs and suits have evolved over time, with diamonds, hearts, clubs, and spades becoming standard. Knowing the rich history can make your next game night feel even more meaningful!

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