Question

A fair coin is tossed three times. What is the probability that the sequence of tosses is HTH? Write your answer as a fraction or a decimal, rounded to four decimal places.

Answer 1

To find the probability of obtaining the specific sequence HTH when tossing a fair coin three times, we can follow these steps:

1. **Understand the Total Outcomes**: When a fair coin is tossed, there are two possible results for each toss: Heads (H) or Tails (T). Since the coin is tossed three times, the total number of outcomes is given by:
\[
2^3 = 8
\]

The possible sequences are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

2. **Identify the Favorable Outcome**: We are interested in one specific outcome: HTH.

3. **Calculate the Probability**: The probability of a specific outcome happening is calculated as the number of favorable outcomes divided by the total number of outcomes. Since there is only one favorable outcome (HTH), the probability \( P \) is:
\[
P(\text{HTH}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{8}
\]

4. **Convert the Fraction to Decimal**: To express this as a decimal:
\[
\frac{1}{8} = 0.125
\]

5. **Round to Four Decimal Places**: The final step is to round 0.125 to four decimal places:
\[
0.1250
\]

Thus, the probability that the sequence of tosses is HTH is:

\[
\boxed{0.1250}
\]