Final answer:
The sample space for the experiment with both the die roll and coin tosses includes 18 outcomes, such as 1H, 1T, 2HH, 2HT, and so on. The probability of rolling a 2 on the die and getting two tails (2TT) from the coin tosses is 1/18, as there is only one such outcome in the complete sample space.
Step-by-step explanation:
Experiment Sample Space and Probability Calculation
When performing an experiment where a regular die is rolled and depending on the result a coin is tossed either once or twice, we have a compound experiment with two stages, and the sample space needs to account for all possible outcomes from both stages of the experiment.
Considering a six-sided die with faces {1, 2, 3, 4, 5, 6}, the sample space for rolling the die is this set of numbers. For each odd number (1, 3, and 5), the coin is tossed once, with possible outcomes being {H, T}. For each even number (2, 4, and 6), the coin is tossed twice, with possible outcomes being {HH, HT, TH, TT}. Combining these, we have a sample space for this experiment as follows:
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- 1H, 1T
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- 2HH, 2HT, 2TH, 2TT
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- 3H, 3T
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- 4HH, 4HT, 4TH, 4TT
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- 5H, 5T
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- 6HH, 6HT, 6TH, 6TT
Now, to find the probability of getting a number 2 and two tails (2TT), we can calculate it by considering that there is only one outcome of 2TT in the sample space, and there are a total of 12 possible outcomes from tossing the coin (1 toss for each odd number and 2 tosses for each even number), resulting in a sample space of 18 outcomes when combined with the die roll. Hence, the probability P(getting a number 2 and two tails) = 1/18.