Question

A fair coin is flipped twice.

What is the probability of getting at least one heads?
(4 Points)

1/4

1/2

3/4

1

Answer 1

To find the probability of getting at least one heads when flipping a fair coin twice, it is often easier to first calculate the probability of the complementary event (getting no heads at all) and then subtract that from 1.

1. **Determine the total outcomes when flipping the coin twice:**
The total outcomes are:
- HH (Heads, Heads)
- HT (Heads, Tails)
- TH (Tails, Heads)
- TT (Tails, Tails)

So, there are 4 possible outcomes.

2. **Calculate the event of getting no heads:**
The only outcome that results in no heads is:
- TT (Tails, Tails)

Thus, there is 1 outcome that results in no heads.

3. **Calculate the probability of getting no heads:**
\[
P(\text{no heads}) = \frac{\text{number of no heads outcomes}}{\text{total outcomes}} = \frac{1}{4}
\]

4. **Calculate the probability of getting at least one heads:**
\[
P(\text{at least one heads}) = 1 - P(\text{no heads}) = 1 - \frac{1}{4} = \frac{3}{4}
\]

Therefore, the probability of getting at least one heads when flipping a fair coin twice is \(\frac{3}{4}\).

The correct answer is:
**3/4**.