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A team of 8 couples, (husband and wife) attend a lucky draw in which 4 persons picked up for a prize. The probability that there is at least one couple is
- a)11/39
- b)15/39
- c)14/39
- d)12/39
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A team of 8couples, (husband and wife) attend a lucky draw in which 4p...
8 couples are there out of which 4 persons are picked for a prize.
P (At least one couple in 4)=1−P ( No Couple in 4)
P(No couple in 4) =
P(No couple in 4) =
P(At Least one couple in 4) =
P (At least one couple in 4)=1−P ( No Couple in 4)
P(No couple in 4) =
P(No couple in 4) =
P(At Least one couple in 4) =
Community Answer
A team of 8couples, (husband and wife) attend a lucky draw in which 4p...
To solve this problem, we need to calculate the probability that at least one couple is picked for the prize out of 4 randomly chosen people from a team of 8 couples.
Let's break down the problem into smaller steps:
Step 1: Calculate the total number of ways to choose 4 people out of 16 (8 couples).
The total number of ways to choose 4 people out of 16 can be calculated using the combination formula:
C(16, 4) = 16! / (4! * (16-4)!) = 16! / (4! * 12!) = (16 * 15 * 14 * 13) / (4 * 3 * 2 * 1) = 1820
So, there are 1820 possible ways to choose 4 people out of 16.
Step 2: Calculate the number of ways to choose 4 people with no couples.
To choose 4 people with no couples, we need to select 4 individuals from 8 couples. This can be done in the following ways:
C(8, 4) = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70
So, there are 70 ways to choose 4 individuals without any couples.
Step 3: Calculate the probability of selecting at least one couple.
The probability of selecting at least one couple can be calculated by subtracting the probability of selecting no couples from 1.
P(at least one couple) = 1 - P(no couples)
P(no couples) = number of ways to choose 4 individuals with no couples / total number of ways to choose 4 people
P(no couples) = 70 / 1820 = 1 / 26
P(at least one couple) = 1 - 1 / 26 = 25 / 26
Therefore, the probability that there is at least one couple in the lucky draw is 25/26 or approximately 0.962.
However, none of the given options match this probability. So, there seems to be an error in the options provided or in the solution.
Let's break down the problem into smaller steps:
Step 1: Calculate the total number of ways to choose 4 people out of 16 (8 couples).
The total number of ways to choose 4 people out of 16 can be calculated using the combination formula:
C(16, 4) = 16! / (4! * (16-4)!) = 16! / (4! * 12!) = (16 * 15 * 14 * 13) / (4 * 3 * 2 * 1) = 1820
So, there are 1820 possible ways to choose 4 people out of 16.
Step 2: Calculate the number of ways to choose 4 people with no couples.
To choose 4 people with no couples, we need to select 4 individuals from 8 couples. This can be done in the following ways:
C(8, 4) = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70
So, there are 70 ways to choose 4 individuals without any couples.
Step 3: Calculate the probability of selecting at least one couple.
The probability of selecting at least one couple can be calculated by subtracting the probability of selecting no couples from 1.
P(at least one couple) = 1 - P(no couples)
P(no couples) = number of ways to choose 4 individuals with no couples / total number of ways to choose 4 people
P(no couples) = 70 / 1820 = 1 / 26
P(at least one couple) = 1 - 1 / 26 = 25 / 26
Therefore, the probability that there is at least one couple in the lucky draw is 25/26 or approximately 0.962.
However, none of the given options match this probability. So, there seems to be an error in the options provided or in the solution.
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A team of 8couples, (husband and wife) attend a lucky draw in which 4persons picked up for a prize. The probability that there is at least one couple isa)11/39b)15/39c)14/39d)12/39Correct answer is option 'B'. Can you explain this answer?
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A team of 8couples, (husband and wife) attend a lucky draw in which 4persons picked up for a prize. The probability that there is at least one couple isa)11/39b)15/39c)14/39d)12/39Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A team of 8couples, (husband and wife) attend a lucky draw in which 4persons picked up for a prize. The probability that there is at least one couple isa)11/39b)15/39c)14/39d)12/39Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A team of 8couples, (husband and wife) attend a lucky draw in which 4persons picked up for a prize. The probability that there is at least one couple isa)11/39b)15/39c)14/39d)12/39Correct answer is option 'B'. Can you explain this answer?.
A team of 8couples, (husband and wife) attend a lucky draw in which 4persons picked up for a prize. The probability that there is at least one couple isa)11/39b)15/39c)14/39d)12/39Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A team of 8couples, (husband and wife) attend a lucky draw in which 4persons picked up for a prize. The probability that there is at least one couple isa)11/39b)15/39c)14/39d)12/39Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A team of 8couples, (husband and wife) attend a lucky draw in which 4persons picked up for a prize. The probability that there is at least one couple isa)11/39b)15/39c)14/39d)12/39Correct answer is option 'B'. Can you explain this answer?.
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