Question

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Part 1
If you toss a fair coin 4 ​times, what is the probability of getting all tails​?

Answer 1

To calculate the probability of getting all tails when tossing a fair coin 4 times, we can follow these steps:

1. **Determine the number of outcomes for each toss**: A fair coin has 2 possible outcomes (heads or tails).

2. **Calculate the total number of outcomes for 4 tosses**: For 4 tosses, the total number of outcomes is given by \(2^4\):
\[
2^4 = 16
\]

3. **Identify the number of favorable outcomes**: There is only 1 favorable outcome for getting all tails (TTTT).

4. **Calculate the probability**: The probability \(P\) of getting all tails is the ratio of the number of favorable outcomes to the total number of outcomes:
\[
P(\text{all tails}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{16}
\]

Therefore, the probability of getting all tails when tossing a fair coin 4 times is \(\frac{1}{16}\).