To determine the probability of getting three tails in three tosses of a fair coin, let's break down the steps in detail:
1. Understanding the Probability of a Single Toss:
- For a fair coin, there are two possible outcomes in any single toss: heads (H) or tails (T).
- Each outcome (heads or tails) has an equal probability of occurring, which is [tex]\(\frac{1}{2}\)[/tex].
2. Probability of Tails in One Toss:
- The probability of getting tails (T) in one toss of a fair coin is [tex]\(\frac{1}{2}\)[/tex].
3. Independent Events:
- The tosses of a coin are independent events. This means the outcome of one toss does not affect the outcome of another toss.
4. Calculating Combined Probability:
- To find the probability of getting tails in three consecutive tosses, we multiply the probability of getting tails in each individual toss.
- So, we have:
[tex]\[
P(\text{three tails}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right)
\][/tex]
5. Performing the Multiplication:
- Multiply the fractions:
[tex]\[
P(\text{three tails}) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}
\][/tex]
Thus, the probability of tossing three tails in three attempts with a fair coin is [tex]\(\frac{1}{8}\)[/tex].
So, the correct answer is [tex]\(\frac{1}{8}\)[/tex].
