Bob has a peculiar pair of tetrahedral (four-sided) dice. When he rolls the dice, the probability of any particular outcome is proportional to the sum of the readings on the individual dice. In particular, letting K represent the sum, then K = K₁ + K₂, where K₁ and K₂ denote the readings on Die 1 and Die 2, respectively.

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Bob has a peculiar pair of tetrahedral (four-sided) dice. When he rolls the dice, the
probability of any particular outcome is proportional to the sum of the readings on the
individual dice. In particular, letting K represent the sum, then K = K₁ + K2, where K₁
and K₂ denote the readings on Die 1 and Die 2, respectively.
Assume that all outcomes corresponding to a particular sum are equally likely.
Transcribed Image Text:Bob has a peculiar pair of tetrahedral (four-sided) dice. When he rolls the dice, the probability of any particular outcome is proportional to the sum of the readings on the individual dice. In particular, letting K represent the sum, then K = K₁ + K2, where K₁ and K₂ denote the readings on Die 1 and Die 2, respectively. Assume that all outcomes corresponding to a particular sum are equally likely.
Determine the probability of rolling a double.
What is the probability that Bob rolls a 2 and a 3, in either order?
Determine the probability that K₁ and K₂ are at least one number apart. That is,
determine P(|K₁ − K₂| ≥ 1).
Transcribed Image Text:Determine the probability of rolling a double. What is the probability that Bob rolls a 2 and a 3, in either order? Determine the probability that K₁ and K₂ are at least one number apart. That is, determine P(|K₁ − K₂| ≥ 1).
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