Question
upstudy study bank question image url

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

Ask by Sherman Hamilton. in the United States
Mar 09,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The probability is \( \frac{3}{4} \).

Solution

1. The total number of cards in the deck is \(52\). 2. The number of diamond cards in the deck is \(13\). 3. Therefore, the number of non-diamond cards is \(52 - 13 = 39\). 4. The probability of being dealt a non-diamond card is \[ \frac{39}{52}. \] 5. Simplify the fraction by dividing the numerator and the denominator by \(13\): \[ \frac{39 \div 13}{52 \div 13} = \frac{3}{4}. \] The probability is \( \frac{3}{4} \).

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Extra Insights

In a standard 52-card deck, there are 13 diamonds. To find the probability of not being dealt a diamond, we first calculate the number of non-diamond cards, which is 52 - 13 = 39. Therefore, the probability of not being dealt a diamond is the number of non-diamond cards divided by the total number of cards: \[ P(\text{not a diamond}) = \frac{39}{52} = \frac{3}{4}. \] So, the probability is \(\frac{3}{4}\). Did you know that playing cards have a fascinating history? They are believed to have originated in China during the Tang Dynasty as early as the 9th century! The layout of today’s four suits – hearts, diamonds, clubs, and spades – emerged in Europe in the late 15th century. Each suit has its own unique symbolism, making every card a little piece of history! Want a real-world application? Understanding probabilities can be super useful in everyday life, especially in areas like gambling, sports statistics, and risk assessment. For instance, if you're into poker, knowing the odds of drawing certain cards can help you make better decisions during the game. The more informed you are about probabilities, the better your chances of coming out ahead!

Related Questions

Latest Probability Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy