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The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is
- a)1/4
- b)1/2
- c)3/4
- d)1/3
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The probabilities of solving a problem by three student A,B,C are 1/2,...
We have, probability that A can solve the problem = P(A) = 1/2 ,
And in this way P(B) = 1/3 and P(C) = 1/4.
P(A cannot solve the problem) = 1 – P(A) = 1/2 ,
P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,
P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.
P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.
Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)
= 1 – 1/4 = 3/4
And in this way P(B) = 1/3 and P(C) = 1/4.
P(A cannot solve the problem) = 1 – P(A) = 1/2 ,
P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,
P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.
P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.
Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)
= 1 – 1/4 = 3/4
Most Upvoted Answer
The probabilities of solving a problem by three student A,B,C are 1/2,...
The question provides the probabilities of three students, A, B, and C, solving a problem. The probabilities are given as 1/2, 1/3, and 1/4 respectively. We need to find the probability that the problem will be solved.
Let's calculate the probability of the problem not being solved by any of the students. To find this, we need to calculate the probability of each student not solving the problem and then multiply those probabilities together.
The probability that student A does not solve the problem is 1 - 1/2 = 1/2.
The probability that student B does not solve the problem is 1 - 1/3 = 2/3.
The probability that student C does not solve the problem is 1 - 1/4 = 3/4.
Now, let's multiply these probabilities together to find the probability that the problem is not solved by any of the students:
(1/2) * (2/3) * (3/4) = 1/4.
Since we want to find the probability that the problem will be solved, we can subtract the probability of the problem not being solved from 1.
Therefore, the probability that the problem will be solved is:
1 - 1/4 = 3/4.
Hence, the correct answer is option 'C', 3/4.
Let's calculate the probability of the problem not being solved by any of the students. To find this, we need to calculate the probability of each student not solving the problem and then multiply those probabilities together.
The probability that student A does not solve the problem is 1 - 1/2 = 1/2.
The probability that student B does not solve the problem is 1 - 1/3 = 2/3.
The probability that student C does not solve the problem is 1 - 1/4 = 3/4.
Now, let's multiply these probabilities together to find the probability that the problem is not solved by any of the students:
(1/2) * (2/3) * (3/4) = 1/4.
Since we want to find the probability that the problem will be solved, we can subtract the probability of the problem not being solved from 1.
Therefore, the probability that the problem will be solved is:
1 - 1/4 = 3/4.
Hence, the correct answer is option 'C', 3/4.
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The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer?
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