Problem 2. Suppose you have a 6-sided die which is weighted, so that the probability of rolling a '6' is 1/2 (and the other 5 sides of the die have probability 1/10). You roll this die 2 times. Let's define the following events. 1. E₁ is the event that exactly one roll is a '6'. 2. E₂ is the event that the difference between the two rolls is an even number. 3. E3 is the event that both rolls are odd numbers. Please answer the following. (a) What is the cardinality and probability of the event E₁? In notation, calculate |E₁| and P(E₁). (b) What is the cardinality and probability of the event E₁ E₂? In notation, calculate |E₁ E₂] and P(E₁ E₂). (c) What is the cardinality and probability of the event E₁ UE3? In notation, calculate |E₁ U E3 and P(E₁ UE3).

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