When tossing a fair coin, there are 2 possible outcomes for each toss: heads (H) or tails (T). If you toss the coin 3 times, the total number of possible outcomes can be calculated using the formula for the number of outcomes for independent events:
\[ \text{Total outcomes} = 2^n \]
where \( n \) is the number of tosses. In this case, \( n = 3 \):
\[ \text{Total outcomes} = 2^3 = 8 \]
Next, we can list the possible outcomes of the 3 tosses. They are:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT
Among these outcomes, there is only 1 outcome that results in all tails (TTT).
To find the probability of getting all tails, we use the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
Here, the number of favorable outcomes (getting all tails) is 1, and the total outcomes is 8:
\[ \text{Probability of all tails} = \frac{1}{8} \]
Thus, the probability of getting all tails when tossing a fair coin 3 times is:
\[ \frac{1}{8} \text{ or } 0.125 \]
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