JEE Exam > JEE Questions > The probability that a man will live for 10 m...
Start Learning for Free
The probability that a man will live for 10 more years is 1/4 and that his wife will live 10 more years is 1/3. The probability that neither will be alive in 10 years is
- a)5/12
- b)1/2
- c)11/12
- d)7/12
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The probability that a man will live for 10 more years is1/4and that h...
Given probabilities:
- Probability that the man will live for 10 more years = 1/4
- Probability that his wife will live for 10 more years = 1/3
To find: Probability that neither will be alive in 10 years
Solution:
Let A be the event that the man will be alive in 10 years, and B be the event that his wife will be alive in 10 years. Then, the probability that neither will be alive in 10 years is the probability of the complement of the union of A and B, i.e., P((A ∪ B)').
Using the formula for the probability of the union of two events, we have:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
where P(A ∩ B) is the probability that both the man and his wife will be alive in 10 years.
Substituting the given probabilities, we get:
P(A ∪ B) = 1/4 + 1/3 - P(A ∩ B)
Simplifying, we get:
P(A ∩ B) = 7/12 - P((A ∪ B)')
Now, we know that the probability of the man being alive in 10 years is 1/4, which means the probability of him not being alive in 10 years is 3/4. Similarly, the probability of his wife not being alive in 10 years is 2/3.
Using the product rule of probability, we can find the probability of both of them not being alive in 10 years:
P((A ∪ B)') = P(A' ∩ B') = P(A') × P(B') = (3/4) × (2/3) = 1/2
Substituting this value in the above equation, we get:
P(A ∩ B) = 7/12 - 1/2 = 1/12
Therefore, the probability that neither the man nor his wife will be alive in 10 years is:
P((A ∪ B)') = 1 - P(A ∪ B) = 1 - (1/4 + 1/3 - 1/12) = 1/2
Hence, the correct option is (B).
- Probability that the man will live for 10 more years = 1/4
- Probability that his wife will live for 10 more years = 1/3
To find: Probability that neither will be alive in 10 years
Solution:
Let A be the event that the man will be alive in 10 years, and B be the event that his wife will be alive in 10 years. Then, the probability that neither will be alive in 10 years is the probability of the complement of the union of A and B, i.e., P((A ∪ B)').
Using the formula for the probability of the union of two events, we have:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
where P(A ∩ B) is the probability that both the man and his wife will be alive in 10 years.
Substituting the given probabilities, we get:
P(A ∪ B) = 1/4 + 1/3 - P(A ∩ B)
Simplifying, we get:
P(A ∩ B) = 7/12 - P((A ∪ B)')
Now, we know that the probability of the man being alive in 10 years is 1/4, which means the probability of him not being alive in 10 years is 3/4. Similarly, the probability of his wife not being alive in 10 years is 2/3.
Using the product rule of probability, we can find the probability of both of them not being alive in 10 years:
P((A ∪ B)') = P(A' ∩ B') = P(A') × P(B') = (3/4) × (2/3) = 1/2
Substituting this value in the above equation, we get:
P(A ∩ B) = 7/12 - 1/2 = 1/12
Therefore, the probability that neither the man nor his wife will be alive in 10 years is:
P((A ∪ B)') = 1 - P(A ∪ B) = 1 - (1/4 + 1/3 - 1/12) = 1/2
Hence, the correct option is (B).
Free Test
FREE
| Start Free Test |
Community Answer
The probability that a man will live for 10 more years is1/4and that h...
Probability that none of them will live for 10 years = probability of man(not living for 10 more years) *
probability of wife(not living for 10 more years)
P(man living 10 more years)=1/4
P'(man not living 10 more years)= 1-P = 1 - 1/4 = 3/4
Similarly for wife,
P(wife living)=1/3
P'(wife not living)= 1- 1/3 = 2/3
Therefore,
Probability that none of them will live for 10 years = (3/4)*(2/3)
= 1/2
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct answer is option 'B'. Can you explain this answer?
Question Description
The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct 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 The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct 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 The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct answer is option 'B'. Can you explain this answer?.
The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct 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 The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct 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 The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct answer is option 'B'. Can you explain this answer?.
Solutions for The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct 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 The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The probability that a man will live for 10 more years is1/4and that his wife will live 10 more years is1/3.The probability that neither will be alive in 10 years isa)5/12b)1/2c)11/12d)7/12Correct 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