You are dealt one card from a 52-card deck. Find the probability that you are not dealt a ten.
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a ten.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
![**Card Probability Problem**
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a ten.
---
The probability is [ ]. (Type an integer or a fraction. Simplify your answer.)
---
**Explanation:**
In a standard 52-card deck, there are four tens (one from each suit: hearts, diamonds, clubs, and spades). To find the probability of not being dealt a ten, calculate the number of ways to draw a card that is not a ten, which is 52 total cards minus 4 ten cards:
\[
52 - 4 = 48 \text{ non-ten cards}
\]
The probability of not getting a ten is then:
\[
\frac{48}{52}
\]
Simplify the fraction:
\[
\frac{48 \div 4}{52 \div 4} = \frac{12}{13}
\]
Thus, the probability that you are not dealt a ten is \( \frac{12}{13} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a4d4bf4-ffa5-40bf-a4b6-a19d4afcfff5%2Fe71c1c29-2858-4a4a-b45c-d2fafcc240bc%2F1mmjrhl_processed.png&w=3840&q=75)
Transcribed Image Text:**Card Probability Problem**
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a ten.
---
The probability is [ ]. (Type an integer or a fraction. Simplify your answer.)
---
**Explanation:**
In a standard 52-card deck, there are four tens (one from each suit: hearts, diamonds, clubs, and spades). To find the probability of not being dealt a ten, calculate the number of ways to draw a card that is not a ten, which is 52 total cards minus 4 ten cards:
\[
52 - 4 = 48 \text{ non-ten cards}
\]
The probability of not getting a ten is then:
\[
\frac{48}{52}
\]
Simplify the fraction:
\[
\frac{48 \div 4}{52 \div 4} = \frac{12}{13}
\]
Thus, the probability that you are not dealt a ten is \( \frac{12}{13} \).
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