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Question Number 210832 by BaliramKumar last updated on 19/Aug/24

If the probability of A solving a question is 1/2 and the probability of B solving the question is 2/3 then the probability of the question being solved is

If the probability of A solving a question is 1/2 and the probability of B solving the question is 2/3 then the probability of the question being solved is

Commented by mr W last updated on 20/Aug/24

both A and B don′t solve: p=(1−(1/2))×(1−(2/3))=(1/6) at least one of them solves: p=1−(1/6)=(5/6) ✓

bothAandBdon′tsolve:p=(1−12)×(1−23)=16atleastoneofthemsolves:p=1−16=56✓

Answered by Ghisom last updated on 20/Aug/24

the probability it′s not solved by both A and B is (1−(1/2))(1−(2/3))=(1/6) ⇒ the probability it is solved is 1−(1/6)=(5/6)

theprobabilityit′snotsolvedbybothAandBis(1−12)(1−23)=16⇒theprobabilityitissolvedis1−16=56

Answered by BHOOPENDRA last updated on 20/Aug/24

The probability of the question being solved is the probability of at least one of them solving it. We can use the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) where P(A ∪ B) is the probability of the question being solved, P(A) is the probability of A solving it, P(B) is the probability of B solving it, and P(A ∩ B) is the probability of both A and B solving it. Assuming A and B are independent, we have: P(A ∩ B) = P(A) ×P(B) = (1/2) × (2/3) = 1/3 Now, we can plug in the values: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = (1/2) + (2/3) - (1/3) = 1/2 + 1/3 = 5/6 So, the probability of the question being solved is 5/6. To find the probability of the question being unsolved, we can use the complement rule: P(unsolved) = 1 - P(solved) We already found the probability of the question being solved: P(solved) = 5/6 So, the probability of the question being unsolved is: P(unsolved) = 1 - 5/6 = 1/6 Therefore, the probability of the question being unsolved is 1/6.

The probability of the question being solved is the probability of at least one of them solving it. We can use the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) where P(A ∪ B) is the probability of the question being solved, P(A) is the probability of A solving it, P(B) is the probability of B solving it, and P(A ∩ B) is the probability of both A and B solving it. Assuming A and B are independent, we have: P(A ∩ B) = P(A) ×P(B) = (1/2) × (2/3) = 1/3 Now, we can plug in the values: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = (1/2) + (2/3) - (1/3) = 1/2 + 1/3 = 5/6 So, the probability of the question being solved is 5/6. To find the probability of the question being unsolved, we can use the complement rule: P(unsolved) = 1 - P(solved) We already found the probability of the question being solved: P(solved) = 5/6 So, the probability of the question being unsolved is: P(unsolved) = 1 - 5/6 = 1/6 Therefore, the probability of the question being unsolved is 1/6.

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