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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?
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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?
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