Question: Suppose a dice was rolled two times and the minimum number of dots of the dices facing up was observed. For example, if one dice

Suppose a dice was rolled two times and the minimum number of dots of the dices facing up was observed. For example, if one dice shows 3-dot and another dice shows 4-dot, the minimum number of dots is 3, or if one dice shows 1-dot and another dice shows 1-dot, the minimum number of dots is 1. Based on the observed minimum number of dots a fair coin is tossed and the total number of tails is counted. Given the minimum number of dots facing up is even, what is the probability the first and the last position of the coin tossing will be tail?

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