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15 Feb 2021, 18:50
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Shoot I rushed. There are three possibilities here.
LLR : 1/2 x 1/2 x 1/2 = 1/8
LRL : 1/2 x 1/2 x 1/2 = 1/8
RLL : 1/2 x 1/2 x 1/2 = 1/8
At each fork in the road, the probability is obviously 1/2
1/8 + 1/8 + 1/8 = 3/8
D.
LLR : 1/2 x 1/2 x 1/2 = 1/8
LRL : 1/2 x 1/2 x 1/2 = 1/8
RLL : 1/2 x 1/2 x 1/2 = 1/8
At each fork in the road, the probability is obviously 1/2
1/8 + 1/8 + 1/8 = 3/8
D.
26 Feb 2022, 06:14
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ugo_castelo
The sieve is symmetric about the center.
Without doing much math can guesstimate with reasonable chance of success.
Slots 2&3 should have equal probability, slots 1&4 equal but less than the others.
2&3 could be weighted 2 and the others 1, so slot 2 could have probability of 2/6, but this doesn't appear as an answer.
2&3 could be weighted 3 and the others 1, so slot 2 could be 3/8.
A. can be eliminated because 2&3 together would add to 1/8, meaning the other two are 7/8, not possible given that a casual examination shows fewer ways to reach these slots.
B. can be eliminated for the same reason.
C. can be eliminated because it implies equal probability for all slots, not possible.
E. can be eliminated because it implies 0 probability for slots 1&4.
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06 Jul 2024, 09:12
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thewind
I think this is the best solution.
We can say simply by symmetry that number of scenarios in which ball goes into 1 is the same as that of 4, and the number of scenarios in which the ball goes into 2 is the same as that of 3.
We can see that there is only 1 scenario in which ball goes into pocket 1. So that means there is also only 1 scenario in which ball goes into pocket 4. That leaves 6 scenarios equally distributed between pocket 2 and pocket 3.
