Let's calculate the probability of getting exactly 2 heads and 1 tail when flipping three coins. Here's a detailed, step-by-step solution:
### Step-by-Step Solution:
1. Identify the Favorable Outcomes:
- When we flip three coins, we want to find the number of outcomes that result in exactly 2 heads (H) and 1 tail (T).
- The favorable outcomes are:
- HHT
- HTH
- THH
- Therefore, there are 3 favorable outcomes.
2. Calculate the Total Number of Possible Outcomes:
- Each coin flip has 2 possible outcomes: heads (H) or tails (T).
- Since there are 3 coins, the total number of possible outcomes is given by the product of the possible outcomes for each coin flip.
[tex]\[
\text{Total possible outcomes} = 2 \times 2 \times 2 = 8
\][/tex]
- Thus, there are 8 total possible outcomes when flipping three coins.
3. Calculate the Probability:
- Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{8}
\][/tex]
Therefore, the probability of getting exactly 2 heads and 1 tail when flipping three coins is:
[tex]\(\frac{3}{8}\)[/tex].
### Conclusion:
The correct answer is:
[tex]\[
\frac{3}{8}
\][/tex]
