JEE Exam > JEE Questions > Two cards are drawn at random from a pack of ...
Start Learning for Free
Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two cards are drawn at random from a pack of playing cards. Find the p...
The total number of cards in a pack of playing cards is 52.
There are 4 suits in a deck of cards: hearts, diamonds, clubs, and spades. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
To find the probability that one card is a heart and the other is an ace, we need to consider two cases:
Case 1: The first card drawn is a heart and the second card drawn is an ace.
- There are 13 hearts in the deck, so the probability of drawing a heart as the first card is 13/52.
- After the first card is drawn, there are 3 aces left in the deck (Ace of hearts, Ace of diamonds, Ace of clubs), so the probability of drawing an ace as the second card is 3/51 (since there are now only 51 cards left in the deck).
- Therefore, the probability of this case is (13/52) * (3/51) = 1/68.
Case 2: The first card drawn is an ace and the second card drawn is a heart.
- There are 4 aces in the deck, so the probability of drawing an ace as the first card is 4/52.
- After the first card is drawn, there are 12 hearts left in the deck, so the probability of drawing a heart as the second card is 12/51.
- Therefore, the probability of this case is (4/52) * (12/51) = 1/221.
To find the total probability, we need to add the probabilities of both cases together:
1/68 + 1/221 = 289/15228 = 1/52.
Therefore, the probability that one card is a heart and the other is an ace is 1/52.
The correct answer is option 'B' - 1/26.
There are 4 suits in a deck of cards: hearts, diamonds, clubs, and spades. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
To find the probability that one card is a heart and the other is an ace, we need to consider two cases:
Case 1: The first card drawn is a heart and the second card drawn is an ace.
- There are 13 hearts in the deck, so the probability of drawing a heart as the first card is 13/52.
- After the first card is drawn, there are 3 aces left in the deck (Ace of hearts, Ace of diamonds, Ace of clubs), so the probability of drawing an ace as the second card is 3/51 (since there are now only 51 cards left in the deck).
- Therefore, the probability of this case is (13/52) * (3/51) = 1/68.
Case 2: The first card drawn is an ace and the second card drawn is a heart.
- There are 4 aces in the deck, so the probability of drawing an ace as the first card is 4/52.
- After the first card is drawn, there are 12 hearts left in the deck, so the probability of drawing a heart as the second card is 12/51.
- Therefore, the probability of this case is (4/52) * (12/51) = 1/221.
To find the total probability, we need to add the probabilities of both cases together:
1/68 + 1/221 = 289/15228 = 1/52.
Therefore, the probability that one card is a heart and the other is an ace is 1/52.
The correct answer is option 'B' - 1/26.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer?
Question Description
Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer?.
Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer?.
Solutions for Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace. [REE 2001 (Mains)] a)2/26 b)1/26 c)3/26 d)4/26 Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup