Quant Exam > Quant Questions > From a pack of 52 cards, 2 cards are drawn at...
Start Learning for Free
From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?
- a)55/221
- b)52/225
- c)44/221
- d)48/221
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
From a pack of 52 cards, 2 cards are drawn at random. What is the prob...
Prob. of both red = 26C2 / 52C2
Prob. of both kings = 4C2 / 52C2
Since there are also cads which are both red and king, so we will subtract there prob.
There are 2 red cards which are kings
Prob. of both red and king = 2C2 / 52C2
So required prob. = 26C2 / 52C2 + 4C2 / 52C2 – 2C2 / 52C2
Prob. of both kings = 4C2 / 52C2
Since there are also cads which are both red and king, so we will subtract there prob.
There are 2 red cards which are kings
Prob. of both red and king = 2C2 / 52C2
So required prob. = 26C2 / 52C2 + 4C2 / 52C2 – 2C2 / 52C2
Most Upvoted Answer
From a pack of 52 cards, 2 cards are drawn at random. What is the prob...
Understanding the Problem
To find the probability that either both cards drawn are red or both are kings from a standard deck of 52 cards, we will use the principle of inclusion-exclusion.
Step 1: Calculate the Probability of Drawing Two Red Cards
- There are 26 red cards in a deck (13 hearts and 13 diamonds).
- The number of ways to choose 2 red cards is given by the combination formula:
\[
C(26, 2) = \frac{26!}{2!(26-2)!} = \frac{26 \times 25}{2} = 325
\]
- The total number of ways to choose any 2 cards from 52 is:
\[
C(52, 2) = \frac{52!}{2!(52-2)!} = \frac{52 \times 51}{2} = 1326
\]
- Thus, the probability of drawing 2 red cards is:
\[
P(\text{2 red}) = \frac{325}{1326}
\]
Step 2: Calculate the Probability of Drawing Two Kings
- There are 4 kings in the deck.
- The number of ways to choose 2 kings is:
\[
C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2} = 6
\]
- Therefore, the probability of drawing 2 kings is:
\[
P(\text{2 kings}) = \frac{6}{1326}
\]
Step 3: Calculate the Probability of Both Events Occurring
- Since there are no red kings, the events are mutually exclusive, and we can simply add the probabilities:
\[
P(\text{2 red or 2 kings}) = P(\text{2 red}) + P(\text{2 kings}) = \frac{325}{1326} + \frac{6}{1326} = \frac{331}{1326}
\]
Step 4: Simplifying the Probability
- Now, simplify \(\frac{331}{1326}\):
\[
P = \frac{331}{1326} = \frac{55}{221}
\]
Thus, the correct answer is option 'A': \(\frac{55}{221}\).
To find the probability that either both cards drawn are red or both are kings from a standard deck of 52 cards, we will use the principle of inclusion-exclusion.
Step 1: Calculate the Probability of Drawing Two Red Cards
- There are 26 red cards in a deck (13 hearts and 13 diamonds).
- The number of ways to choose 2 red cards is given by the combination formula:
\[
C(26, 2) = \frac{26!}{2!(26-2)!} = \frac{26 \times 25}{2} = 325
\]
- The total number of ways to choose any 2 cards from 52 is:
\[
C(52, 2) = \frac{52!}{2!(52-2)!} = \frac{52 \times 51}{2} = 1326
\]
- Thus, the probability of drawing 2 red cards is:
\[
P(\text{2 red}) = \frac{325}{1326}
\]
Step 2: Calculate the Probability of Drawing Two Kings
- There are 4 kings in the deck.
- The number of ways to choose 2 kings is:
\[
C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2} = 6
\]
- Therefore, the probability of drawing 2 kings is:
\[
P(\text{2 kings}) = \frac{6}{1326}
\]
Step 3: Calculate the Probability of Both Events Occurring
- Since there are no red kings, the events are mutually exclusive, and we can simply add the probabilities:
\[
P(\text{2 red or 2 kings}) = P(\text{2 red}) + P(\text{2 kings}) = \frac{325}{1326} + \frac{6}{1326} = \frac{331}{1326}
\]
Step 4: Simplifying the Probability
- Now, simplify \(\frac{331}{1326}\):
\[
P = \frac{331}{1326} = \frac{55}{221}
\]
Thus, the correct answer is option 'A': \(\frac{55}{221}\).
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer?
Question Description
From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer?.
From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?a)55/221b)52/225c)44/221d)48/221e)None of theseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup