CAT Exam > CAT Questions > Sindya draws two cards at random from a pack...
Start Learning for Free
Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards is
- a)25/663
- b)28/663
- c)50/663
- d)2/663
- e)None of the Above
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Sindya draws two cards at random from a pack of cards. After returnin...
Sindya can draw any two cards. Now Bindya has to choose exactly one same card of Sindya's card. This can be done in 2C1 ways.
Remaining 1 card can be drawn in 50C1 ways
So, number of favorable cases = 2 × 50
Total number of case = 50C2 = 26×51
Most Upvoted Answer
Sindya draws two cards at random from a pack of cards. After returnin...
To find the probability that Sindya and Bindya have exactly one common card, we need to consider two scenarios:
1. Sindya draws a card, and Bindya does not draw the same card.
2. Sindya does not draw a card, and Bindya draws the same card.
Let's calculate the probability for each scenario:
Scenario 1:
1. The probability that Sindya draws a card is 1 (since there are 52 cards in the pack and she can choose any card).
2. The probability that Bindya does not draw the same card is (51/52) (since there are 51 cards remaining in the pack and only one of them is the same card Sindya drew).
Therefore, the probability for scenario 1 is (1 * 51/52).
Scenario 2:
1. The probability that Sindya does not draw a card is (51/52) (since there are 51 cards remaining in the pack and she did not draw any).
2. The probability that Bindya draws the same card is (1/52) (since there is only one card in the pack that is the same as the one Sindya did not draw).
Therefore, the probability for scenario 2 is ((51/52) * (1/52)).
Since the two scenarios are mutually exclusive (they cannot happen at the same time), we can add their probabilities to find the total probability that Sindya and Bindya have exactly one common card:
Total probability = (1 * 51/52) + ((51/52) * (1/52))
= 51/52 + 51/2704
= (51 * 2704 + 52 * 51) / 52 * 2704
= (137904 + 2652) / 140608
= 140556 / 140608
= 50/663
Therefore, the probability that Sindya and Bindya have exactly one common card is 50/663, which corresponds to option C.
1. Sindya draws a card, and Bindya does not draw the same card.
2. Sindya does not draw a card, and Bindya draws the same card.
Let's calculate the probability for each scenario:
Scenario 1:
1. The probability that Sindya draws a card is 1 (since there are 52 cards in the pack and she can choose any card).
2. The probability that Bindya does not draw the same card is (51/52) (since there are 51 cards remaining in the pack and only one of them is the same card Sindya drew).
Therefore, the probability for scenario 1 is (1 * 51/52).
Scenario 2:
1. The probability that Sindya does not draw a card is (51/52) (since there are 51 cards remaining in the pack and she did not draw any).
2. The probability that Bindya draws the same card is (1/52) (since there is only one card in the pack that is the same as the one Sindya did not draw).
Therefore, the probability for scenario 2 is ((51/52) * (1/52)).
Since the two scenarios are mutually exclusive (they cannot happen at the same time), we can add their probabilities to find the total probability that Sindya and Bindya have exactly one common card:
Total probability = (1 * 51/52) + ((51/52) * (1/52))
= 51/52 + 51/2704
= (51 * 2704 + 52 * 51) / 52 * 2704
= (137904 + 2652) / 140608
= 140556 / 140608
= 50/663
Therefore, the probability that Sindya and Bindya have exactly one common card is 50/663, which corresponds to option C.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer?
Question Description
Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer?.
Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Sindya draws two cards at random from a pack of cards. After returning them to the pack and shuffling it Bindya draws two cards at random. The probability that they have exactly one common cards isa)25/663b)28/663c)50/663d)2/663e)None of the AboveCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup