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A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.
- a)13/20
- b)17/20
- c)3/20
- d)7/20
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A student can solve 70% problems of a book and second student solve 50...
Probability that first and second student can solve
=0.7×0.5=0.35
Probability that first can solve and second cannot solve
=0.7×0.5=0.35
Probability that first cannot solve and Amisha can solve
=0.3×0.5=0.15
Therefore, probability that at least one of them will solve
=0.35+0.35+0.15 = 0.85
=> 85/100
= 17/20
=0.7×0.5=0.35
Probability that first can solve and second cannot solve
=0.7×0.5=0.35
Probability that first cannot solve and Amisha can solve
=0.3×0.5=0.15
Therefore, probability that at least one of them will solve
=0.35+0.35+0.15 = 0.85
=> 85/100
= 17/20
Most Upvoted Answer
A student can solve 70% problems of a book and second student solve 50...
Solution:
Given, the first student solves 70% of the problems and the second student solves 50% of the problems.
Let A be the event that the first student solves a selected problem and B be the event that the second student solves a selected problem.
Then, the probability that at least one of them will solve a selected problem is given by P(A ∪ B).
Using the formula for the union of two events, we have
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
where P(A) is the probability that the first student solves a selected problem, P(B) is the probability that the second student solves a selected problem, and P(A ∩ B) is the probability that both of them solve a selected problem.
We know that P(A) = 0.7 and P(B) = 0.5.
To find P(A ∩ B), we note that both students can solve a selected problem only if the selected problem is solved by both of them. Therefore, P(A ∩ B) = P(A) × P(B) = 0.7 × 0.5 = 0.35.
Substituting these values in the formula, we get
P(A ∪ B) = 0.7 + 0.5 - 0.35 = 0.85
Therefore, the probability that at least one of them will solve a selected problem is 0.85 or 17/20.
Hence, the correct answer is option (B).
Given, the first student solves 70% of the problems and the second student solves 50% of the problems.
Let A be the event that the first student solves a selected problem and B be the event that the second student solves a selected problem.
Then, the probability that at least one of them will solve a selected problem is given by P(A ∪ B).
Using the formula for the union of two events, we have
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
where P(A) is the probability that the first student solves a selected problem, P(B) is the probability that the second student solves a selected problem, and P(A ∩ B) is the probability that both of them solve a selected problem.
We know that P(A) = 0.7 and P(B) = 0.5.
To find P(A ∩ B), we note that both students can solve a selected problem only if the selected problem is solved by both of them. Therefore, P(A ∩ B) = P(A) × P(B) = 0.7 × 0.5 = 0.35.
Substituting these values in the formula, we get
P(A ∪ B) = 0.7 + 0.5 - 0.35 = 0.85
Therefore, the probability that at least one of them will solve a selected problem is 0.85 or 17/20.
Hence, the correct answer is option (B).
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A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer?
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