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The odds in favour of A solving a problem is 5:7 and Odds against B solving the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?
- a)117/180
- b)181/200
- c)147/180
- d)119/180
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The odds in favour of A solving a problem is 5:7 and Odds against B so...
Given information:
Odds in favour of A solving the problem = 5:7
Odds against B solving the problem = 9:6
To find: Probability that if both of them try, the problem will be solved.
Solution:
Let the probability of A solving the problem be P(A) and the probability of B not solving the problem be P(B').
Then, according to the given information:
P(A) = 5/12 (since odds in favour of A = 5:7)
P(B') = 6/15 = 2/5 (since odds against B = 9:6)
The probability that either A solves the problem or B doesn't solve the problem can be found using the formula:
P(A or B') = P(A) + P(B') - P(A and B')
Now, we need to find the probability of both A and B solving the problem. Let this probability be P(A and B).
We know that P(A and B) = P(A) * P(B) (assuming A and B are independent events)
To find P(B), we can use the fact that the odds against B solving the problem are 9:6, which means the probability of B solving the problem is:
P(B) = 6/15 = 2/5
Therefore, we can substitute the values of P(A), P(B), and P(A and B) in the above formula to get:
P(A or B') = P(A) + P(B') - P(A and B)
=> P(A and B) = P(A) + P(B') - P(A or B')
=> P(A and B) = 5/12 + 3/5 - P(A or B')
Now, we need to find P(A or B'). We can use the fact that A and B are mutually exclusive events, i.e., they cannot happen at the same time. Therefore:
P(A or B') = P(A) + P(B')
=> P(A or B') = 5/12 + 2/5
=> P(A or B') = 37/60
Substituting this value in the above equation, we get:
P(A and B) = 5/12 + 3/5 - 37/60
=> P(A and B) = 13/60
Therefore, the probability that if both of them try, the problem will be solved is:
P(A and B) = 13/60
Hence, the correct answer is option (A) 117/180. However, the answer provided is incorrect.
Odds in favour of A solving the problem = 5:7
Odds against B solving the problem = 9:6
To find: Probability that if both of them try, the problem will be solved.
Solution:
Let the probability of A solving the problem be P(A) and the probability of B not solving the problem be P(B').
Then, according to the given information:
P(A) = 5/12 (since odds in favour of A = 5:7)
P(B') = 6/15 = 2/5 (since odds against B = 9:6)
The probability that either A solves the problem or B doesn't solve the problem can be found using the formula:
P(A or B') = P(A) + P(B') - P(A and B')
Now, we need to find the probability of both A and B solving the problem. Let this probability be P(A and B).
We know that P(A and B) = P(A) * P(B) (assuming A and B are independent events)
To find P(B), we can use the fact that the odds against B solving the problem are 9:6, which means the probability of B solving the problem is:
P(B) = 6/15 = 2/5
Therefore, we can substitute the values of P(A), P(B), and P(A and B) in the above formula to get:
P(A or B') = P(A) + P(B') - P(A and B)
=> P(A and B) = P(A) + P(B') - P(A or B')
=> P(A and B) = 5/12 + 3/5 - P(A or B')
Now, we need to find P(A or B'). We can use the fact that A and B are mutually exclusive events, i.e., they cannot happen at the same time. Therefore:
P(A or B') = P(A) + P(B')
=> P(A or B') = 5/12 + 2/5
=> P(A or B') = 37/60
Substituting this value in the above equation, we get:
P(A and B) = 5/12 + 3/5 - 37/60
=> P(A and B) = 13/60
Therefore, the probability that if both of them try, the problem will be solved is:
P(A and B) = 13/60
Hence, the correct answer is option (A) 117/180. However, the answer provided is incorrect.
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The odds in favour of A solving a problem is 5:7 and Odds against B solving the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?a)117/180b)181/200c)147/180d)119/180Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The odds in favour of A solving a problem is 5:7 and Odds against B solving the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?a)117/180b)181/200c)147/180d)119/180Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The odds in favour of A solving a problem is 5:7 and Odds against B solving the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?a)117/180b)181/200c)147/180d)119/180Correct answer is option 'A'. Can you explain this answer?.
The odds in favour of A solving a problem is 5:7 and Odds against B solving the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?a)117/180b)181/200c)147/180d)119/180Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The odds in favour of A solving a problem is 5:7 and Odds against B solving the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?a)117/180b)181/200c)147/180d)119/180Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The odds in favour of A solving a problem is 5:7 and Odds against B solving the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?a)117/180b)181/200c)147/180d)119/180Correct answer is option 'A'. Can you explain this answer?.
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