Suppose that you roll two fair dice, and that the dice are independent. Define three events as follows: E1? : Exactly one die shows a number smaller than three. E2? : The absolute value of the difference between the numbers shown by the dice is at most two. E3? : Exactly one die shows the number four. Answer the following questions about this ran

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Suppose that you roll two fair dice, and that the dice are independent. Define three events as follows: E1? : Exactly one die shows a number smaller than three. E2? : The absolute value of the difference between the numbers shown by the dice is at most two. E3? : Exactly one die shows the number four. Answer the following questions about this random experiment: (a) What is P(E1?) ? (b) What is P(E1??E2?) ? (c) What is P(E1??E3?) ? (d) Are events E1? and E3? independent? (e) Are events E1? and E2? independent?

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