Survey: The Loaded Die!

Imagine that you have a loaded die (that’s the singular of ‘dice’). This means the die is biased. It’s not fair. If you roll it, the probability that you’ll get a 44 is higher than the probability of getting any other number. You roll the die a few times and analyze the data.

Decide which of the following is more likely to happen:

A.2,5,3,4,6A. \quad 2, 5, 3, 4, 6 B.4,2,5,3,4,6B. \quad 4, 2, 5, 3, 4, 6

Drop a comment below with your answer, and please do not explain your answer because I don’t want anyone to get influenced by other peoples’ comments. Just a simple AA or a BB will suffice.

I’m going to bed now and when I wake up the next day I hope to see a lot of comments! :)

Until then!

Note by Mursalin Habib
5 years, 1 month ago

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Option 1: A

Upvote this comment if you think it is right.

Daniel Liu - 5 years, 1 month ago

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Option 2: B

Upvote this comment if you think it is right.

Daniel Liu - 5 years, 1 month ago

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Option B

Pranjal Jain - 5 years, 1 month ago

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I say A.

Finn Hulse - 5 years ago

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B

Syed Shamikh Shabbir - 5 years, 1 month ago

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I see it's possible that both are equally likely to happen. But one option cannot be more likely than the other; it's either equally likely or less likely depending on the probability distribution.

Ivan Koswara - 5 years, 1 month ago

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But one option cannot be more likely than the other;

Why is that? If something is less likely to happen then something else, then that something else is more likely to happen than the first something.

Daniel Liu - 5 years, 1 month ago

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I mean one particular option cannot be more likely than the other one, not any one option cannot be more likely. Ambiguity; my bad.

Ivan Koswara - 5 years, 1 month ago

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B

Vinod Chhallany - 5 years, 1 month ago

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Option A

Kavi Scidarth - 5 years, 1 month ago

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@Mursalin Habib It has been a day!

Justin Wong - 5 years, 1 month ago

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A

Yannick Yao - 5 years ago

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Because apparently this one person's "day" meaning 15 days in real world, I decide to screw it and give my reasoning. Here, P(A),P(B),P(4)P(A), P(B), P(4) are probabilities of getting the sequence AA, the sequence BB, and the throw 44 in that order.

AA is more likely. Note that P(B)=P(4)P(A)1P(A)=P(A)P(B) = P(4) \cdot P(A) \le 1 \cdot P(A) = P(A), so the probability of getting BB is less than or equal to AA.

Ivan Koswara - 5 years ago

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