Suppose a fair six-sided die has the following sides: 1, 1, 1, 1, 4, 4. The die is rolled twice. The mixed outcomes [1,4] and [4,1] are considered "successes" while the outcomes [1,1] and [4,4] are considered "failures." What is the expected number of rolls to achieve the first success?
I am having trouble here because the die is rolled twice and am not quite sure how to calculate this expectation.
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