To determine the probability of getting at least one head when tossing a coin three times, we can approach the problem using the concept of complementary probability. This means we first calculate the probability of the opposite event—getting no heads at all—and then subtract that from 1.
1. **Understanding the Coin Tosses**: A single toss of a fair coin has two outcomes: heads (H) or tails (T). When the coin is tossed three times, the total number of possible outcomes is:
Total outcomes = 23 = 8.
The possible sequences of outcomes when tossing the coin three times are:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTY
- TTT
2. **Calculating the Probability of No Heads**: The only outcome where we do not get any heads is the sequence TTT (three tails). Therefore, the probability of getting no heads is:
P(No Heads) = Number of No Heads Outcomes / Total Outcomes = 1 / 8.
3. **Calculating the Probability of At Least One Head**: To find the probability of getting at least one head, we can subtract the probability of getting no heads from 1:
P(At Least One Head) = 1 – P(No Heads) = 1 – (1 / 8) = 7 / 8.
Thus, the probability of getting at least one head when tossing a coin three times is:
P(At Least One Head) = 7/8 or 87.5%.
This means that if you toss a fair coin three times, there is an 87.5% chance that you will see at least one head in your results. This high probability highlights how likely it is to see heads multiple times when tossing a coin relatively few times.