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Suppose you roll two dice and count the number of dots showing. Let A = "the...

Suppose you roll two dice and count the number of dots showing. Let A = "the sum of the dots showing on the two rolls is a prime number."

(a) Let B = "The first toss showed an even number of dots." Are A and B independent? Show your work.

(b) Let C = "the second toss was greater than the first." Are A and C independent? Show your work.

(c) Suppose we pick a value ?k for 1≤?≤61≤k≤6 and let event Dk = "the first toss was greater than or equal to ?.k." For which values of ?k are A and Dk independent? Show your work.

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