Question

A fair coin is flipped twice.

What is the probability of getting at least one heads?

Answer 1

To find the probability of getting at least one heads when a fair coin is flipped twice, we can use the complementary approach. First, we calculate the probability of the opposite event, which is getting no heads (i.e., getting tails on both flips).

1. The possible outcomes when flipping a coin twice are:
- HH (heads on first flip, heads on second flip)
- HT (heads on first flip, tails on second flip)
- TH (tails on first flip, heads on second flip)
- TT (tails on first flip, tails on second flip)

So, there are a total of 4 possible outcomes.

2. The outcome that gives us no heads is TT (tails, tails).

3. The probability of getting tails on one flip is \( \frac{1}{2} \). Therefore, the probability of getting tails on both flips is:
\[
P(TT) = P(T) \times P(T) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\]

4. Now, the probability of getting at least one heads is the complement of getting no heads (i.e., TT):
\[
P(\text{at least one heads}) = 1 - P(TT) = 1 - \frac{1}{4} = \frac{3}{4}
\]

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