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Answer:
The probability is 3/12. The third option is correct.
Step-by-step explanation:
The sample space is
Note that this sample space is not equally probable.
The probability of getting a given number followed is the probability of getting an even number from the 6 numbers (3/6) multiplied by the probability of getting a head after getting that even number, that is 1/2, because is equally probable to get heads or tails from one single coin toss (note that we are assuming that the dice was even, thats why there is a single coin toss).
Therefore, the probability of getting an even number and a head is
P( D in {2,4,6} , H = 1) = P(D in {2,4,6}) * P(H=1 | D in {2,4,6}) = 3/6 * 1/2 = 3/12.