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A problem in Statistics is given to three students A, B and C whose respective chances of solving are 1/3, 1/4, 1/5. Find the probability that: It is solved by exactly 1 of them. a) 1/60 b) 2/5 c) 3/5 d) 13/30?
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A problem in Statistics is given to three students A, B and C whose re...
Solution:
Given, the probability of solving the problem by students A, B, and C are 1/3, 1/4, and 1/5 respectively.
We need to find the probability that the problem is solved by exactly 1 of them.
Let A, B, and C be the events of solving the problem by students A, B, and C respectively.
Then, the probability of solving the problem by exactly 1 of them is given by:
P(exactly 1 of them) = P(A' ∩ B ∩ C') + P(A ∩ B' ∩ C') + P(A' ∩ B' ∩ C)
where A', B', and C' are the complement events of A, B, and C respectively.
Now, we can calculate the probabilities as follows:
P(A) = 1/3, P(B) = 1/4, P(C) = 1/5
P(A' ∩ B ∩ C') = P(B ∩ C') * P(A')
= (P(B) - P(A ∩ B)) * (1 - P(C))
= (1/4 - 1/12) * (4/5)
= 1/15
P(A ∩ B' ∩ C') = P(A ∩ C') * P(B')
= (P(A) - P(A ∩ B)) * (3/5)
= (1/3 - 1/12) * (3/4)
= 1/8
P(A' ∩ B' ∩ C) = P(A' ∩ C) * P(B')
= (1 - P(A) - P(C) + P(A ∩ C)) * (3/4)
= (1 - 1/3 - 1/5 + 1/15) * (3/4)
= 7/60
Therefore,
P(exactly 1 of them) = P(A' ∩ B ∩ C') + P(A ∩ B' ∩ C') + P(A' ∩ B' ∩ C)
= 1/15 + 1/8 + 7/60
= 13/30
Hence, the probability that the problem is solved by exactly 1 of them is 13/30.
Answer: Option (d) 13/30.
Given, the probability of solving the problem by students A, B, and C are 1/3, 1/4, and 1/5 respectively.
We need to find the probability that the problem is solved by exactly 1 of them.
Let A, B, and C be the events of solving the problem by students A, B, and C respectively.
Then, the probability of solving the problem by exactly 1 of them is given by:
P(exactly 1 of them) = P(A' ∩ B ∩ C') + P(A ∩ B' ∩ C') + P(A' ∩ B' ∩ C)
where A', B', and C' are the complement events of A, B, and C respectively.
Now, we can calculate the probabilities as follows:
P(A) = 1/3, P(B) = 1/4, P(C) = 1/5
P(A' ∩ B ∩ C') = P(B ∩ C') * P(A')
= (P(B) - P(A ∩ B)) * (1 - P(C))
= (1/4 - 1/12) * (4/5)
= 1/15
P(A ∩ B' ∩ C') = P(A ∩ C') * P(B')
= (P(A) - P(A ∩ B)) * (3/5)
= (1/3 - 1/12) * (3/4)
= 1/8
P(A' ∩ B' ∩ C) = P(A' ∩ C) * P(B')
= (1 - P(A) - P(C) + P(A ∩ C)) * (3/4)
= (1 - 1/3 - 1/5 + 1/15) * (3/4)
= 7/60
Therefore,
P(exactly 1 of them) = P(A' ∩ B ∩ C') + P(A ∩ B' ∩ C') + P(A' ∩ B' ∩ C)
= 1/15 + 1/8 + 7/60
= 13/30
Hence, the probability that the problem is solved by exactly 1 of them is 13/30.
Answer: Option (d) 13/30.
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A problem in Statistics is given to three students A, B and C whose respective chances of solving are 1/3, 1/4, 1/5. Find the probability that: It is solved by exactly 1 of them. a) 1/60 b) 2/5 c) 3/5 d) 13/30?
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A problem in Statistics is given to three students A, B and C whose respective chances of solving are 1/3, 1/4, 1/5. Find the probability that: It is solved by exactly 1 of them. a) 1/60 b) 2/5 c) 3/5 d) 13/30? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A problem in Statistics is given to three students A, B and C whose respective chances of solving are 1/3, 1/4, 1/5. Find the probability that: It is solved by exactly 1 of them. a) 1/60 b) 2/5 c) 3/5 d) 13/30? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A problem in Statistics is given to three students A, B and C whose respective chances of solving are 1/3, 1/4, 1/5. Find the probability that: It is solved by exactly 1 of them. a) 1/60 b) 2/5 c) 3/5 d) 13/30?.
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