Question

A fair coin is tossed three times. What is P(tossing at least one head)?
one eighth
three eighths
seven eighths
one fourth

Answer 1

To find the probability of tossing at least one head when a fair coin is tossed three times, it is often easier to calculate the complementary probability (the probability of the opposite event) and then subtract that from 1.

1. **Complementary Event**: The complementary event of getting at least one head is getting no heads at all, which means getting all tails.

2. **Probability of Getting Tails**: The probability of getting tails on a single toss of a fair coin is \( \frac{1}{2} \).

3. **Probability of Getting All Tails in 3 Tosses**:
\[
P(\text{all tails}) = \left( \frac{1}{2} \right)^3 = \frac{1}{8}
\]

4. **Probability of Getting at Least One Head**:
\[
P(\text{at least one head}) = 1 - P(\text{all tails}) = 1 - \frac{1}{8} = \frac{7}{8}
\]

Thus, the probability of tossing at least one head when a fair coin is tossed three times is \( \frac{7}{8} \).

So the answer is **seven eighths**.