Explanation
1. Find the probability of each student failing to solve the problem
Let P(A),P(B), and P(C) be the probabilities of solving the problem.
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P(A)=21⟹P(A′)=1−21=21
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P(B)=31⟹P(B′)=1−31=32
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P(C)=41⟹P(C′)=1−41=43
2. Calculate the probability that nobody solves the problem
Since the events are independent, the probability that all three fail is the product of their individual failure probabilities:
P(None solve)=P(A′)×P(B′)×P(C′)
P(None solve)=21×32×43
Multiplying the fractions:
P(None solve)=2×3×41×2×3=246=41
3. Calculate the probability that the problem is solved
The problem is considered "solved" if at least one person succeeds.
P(Problem solved)=1−P(None solve)
Correct Option:
(d) 43
