Explanation
Step 1: Write down the given probabilities
Let P(A), P(B), and P(C) be the probabilities of students A, B, and C solving the problem individually. Since they try to solve it independently, their outcomes are independent events.
Probability of A solving the problem: P(A)=21
Probability of A not solving the problem: P(A′)=1−P(A)=1−21=21
Probability of B not solving the problem: P(B′)=41
Let the probability of C solving the problem be: P(C)=p
Probability of C not solving the problem: P(C′)=1−p
Step 2: Use the property of complementary probability
The problem is solved if at least one of the students solves it. The easiest way to calculate this is by using the complement: the only scenario where the problem is not solved is when all three students fail to solve it.
P(Problem is solved)=1−P(None of them solves it)
P(Problem is solved)=1−[P(A′)⋅P(B′)⋅P(C′)]
Step 3: Substitute the values and solve for p
Given that the total probability of the problem being solved is 6463:
6463=1−(21⋅41⋅(1−p))
Rearranging the terms:
21⋅41⋅(1−p)=1−6463
81⋅(1−p)=641
Multiply both sides by 8:
1−p=648
1−p=81
p=1−81
p=87
Conclusion
The individual probability of student C solving the math problem is 87.
Correct Answer: C
