Die Roll & Coin Toss: Why 42 Possible Outcomes?

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SUMMARY

The experiment involving rolling a fair die twice and tossing a coin if the results are the same yields a total of 42 possible outcomes. This is derived from the 36 outcomes from the two die rolls (6 sides each, resulting in 6 * 6) and an additional 12 outcomes from the coin toss, which occurs only when the die results match. Therefore, the calculation is 30 outcomes from distinct die rolls plus 12 outcomes from matching rolls leading to a coin toss, totaling 42 outcomes.

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A fair die is rolled twice. If the two results are the same, a coin is tossed. Why is the total number of different possible outcomes of this experiment $42$?
 
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6 * 6 = 36, so 30 outcomes are a dice roll and 12 outcomes are a coin toss. 30 + 12 = 42.
 

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