Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > The probabilities of A, B and C solving a pr...
Start Learning for Free
The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)
Correct answer is '25'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/...
Understanding the Problem
To find the probability that exactly one of A, B, or C solves the problem, we need to first determine the probabilities of each individual solving the problem and not solving it.
Given Probabilities
- Probability that A solves: P(A) = 1/3
- Probability that B solves: P(B) = 2/7
- Probability that C solves: P(C) = 3/8
Calculating Not Solving Probabilities
- Probability that A does not solve: P(A') = 1 - P(A) = 2/3
- Probability that B does not solve: P(B') = 1 - P(B) = 5/7
- Probability that C does not solve: P(C') = 1 - P(C) = 5/8
Finding Probabilities for Exactly One Solver
To find the probability that exactly one of them solves the problem, we analyze three scenarios:
1. Only A solves:
Probability = P(A) * P(B') * P(C')
= (1/3) * (5/7) * (5/8)
2. Only B solves:
Probability = P(A') * P(B) * P(C')
= (2/3) * (2/7) * (5/8)
3. Only C solves:
Probability = P(A') * P(B') * P(C)
= (2/3) * (5/7) * (3/8)
Calculating Each Scenario
- For A only:
(1/3) * (5/7) * (5/8) = 25/168
- For B only:
(2/3) * (2/7) * (5/8) = 20/168
- For C only:
(2/3) * (5/7) * (3/8) = 30/168
Total Probability for Exactly One Solver
Now, sum these probabilities:
Total = (25/168) + (20/168) + (30/168) = 75/168 = 25/56
Final Value of x
Since the result is expressed as x/56, we find:
x = 25
Thus, the value of x is 25.
To find the probability that exactly one of A, B, or C solves the problem, we need to first determine the probabilities of each individual solving the problem and not solving it.
Given Probabilities
- Probability that A solves: P(A) = 1/3
- Probability that B solves: P(B) = 2/7
- Probability that C solves: P(C) = 3/8
Calculating Not Solving Probabilities
- Probability that A does not solve: P(A') = 1 - P(A) = 2/3
- Probability that B does not solve: P(B') = 1 - P(B) = 5/7
- Probability that C does not solve: P(C') = 1 - P(C) = 5/8
Finding Probabilities for Exactly One Solver
To find the probability that exactly one of them solves the problem, we analyze three scenarios:
1. Only A solves:
Probability = P(A) * P(B') * P(C')
= (1/3) * (5/7) * (5/8)
2. Only B solves:
Probability = P(A') * P(B) * P(C')
= (2/3) * (2/7) * (5/8)
3. Only C solves:
Probability = P(A') * P(B') * P(C)
= (2/3) * (5/7) * (3/8)
Calculating Each Scenario
- For A only:
(1/3) * (5/7) * (5/8) = 25/168
- For B only:
(2/3) * (2/7) * (5/8) = 20/168
- For C only:
(2/3) * (5/7) * (3/8) = 30/168
Total Probability for Exactly One Solver
Now, sum these probabilities:
Total = (25/168) + (20/168) + (30/168) = 75/168 = 25/56
Final Value of x
Since the result is expressed as x/56, we find:
x = 25
Thus, the value of x is 25.
Free Test
FREE
| Start Free Test |
Community Answer
The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/...
Let E1, E2 and E3 be the events that the problem is solved by A, B and C, respectively. Then,
P(E1) = 1/3, P(E2) = 2/7 and P(E3) = 3/8
Exactly one of A, B and C can solve the problem in the following mutually exclusive ways.
(i) A solves and B and C do not solve.
(ii) B solves and A and C do not solve.
(iii) C solves and A and B do not solve.
Probability that only one will solve the problem
= P(A) and P(not B) and P(not C) + P(not A) and P(B) and P(not C) + P(not A) and P(not B) and P(C)
Attention Electrical Engineering (EE) Students!
To make sure you are not studying endlessly, EduRev has designed Electrical Engineering (EE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electrical Engineering (EE).
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Similar Electrical Engineering (EE) Doubts
Top Courses for Electrical Engineering (EE)View all
The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer?
Question Description
The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer?.
The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer?.
Solutions for The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer?, a detailed solution for The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? has been provided alongside types of The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The probabilities of A, B and C solving a problem are 1/3, 2/7 and 3/8, respectively. If all three try to solve the problem simultaneously, then the probability that exactly one of them will solve it is x/56. Find the value of x. (Answer up to the nearest integer)Correct answer is '25'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) 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
|
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