Question

If you toss a fair coin 3 ​times, what is the probability of getting all tails​?

Answer 1

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:

1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. 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:

\[
\frac{1}{8} \text{ or } 0.125
\]