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A and B are required to solve a problem independently. If 1/2 and 1/3 are their respectively probabilities of solving the problem, then the probability that atleast one of them solves the problem.
  • a)
    1/3
  • b)
    2/3
  • c)
    1/2
  • d)
    1/4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A and B are required to solve a problem independently. If 1/2 and 1/3 ...
Probability that atleast one of them solves the problem = P
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Most Upvoted Answer
A and B are required to solve a problem independently. If 1/2 and 1/3 ...
Understanding the Problem
To find the probability that at least one of A or B solves the problem, we can use the concept of complementary probability.
Step-by-Step Solution
1. Identify Individual Probabilities:
- Probability that A solves the problem: P(A) = 1/2
- Probability that B solves the problem: P(B) = 1/3
2. Calculate the Probability of Neither Solving the Problem:
- Probability that A does not solve the problem: P(A') = 1 - P(A) = 1 - 1/2 = 1/2
- Probability that B does not solve the problem: P(B') = 1 - P(B) = 1 - 1/3 = 2/3
3. Calculate the Probability of Both Not Solving the Problem:
- Since A and B are solving independently, the combined probability of neither solving is:
P(A' and B') = P(A') * P(B') = (1/2) * (2/3) = 1/3
4. Calculate the Probability of At Least One Solving the Problem:
- The probability that at least one of them solves the problem is given by:
P(at least one solves) = 1 - P(A' and B') = 1 - 1/3 = 2/3
Conclusion
Thus, the probability that at least one of A or B solves the problem is 2/3, which corresponds to option B.
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