Question: We have a peculiar fair 4 sided dice with values 1,2,5 and 6. We roll the dice twice. (a) Ethan claims that the event of

We have a peculiar fair 4 sided dice with values 1,2,5 and 6. We roll the dice twice. (a) Ethan claims that the event of the sum of the two rolls being greater than or equal to 10 is at least as likely if we know that the first roll is 5 or 6 than if we know that at least one of the rolls is 5 or 6. Is Ethan correct? Justify your answer. (b) We realize that the dice is not fair. But Ethan makes the same claim as (a). Is he still correct? Justify your answer.

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