To determine how many times you should expect to win if you play a game 20 times, we can use the concept of expected value in probability.
### Step-by-Step Solution:
1. Identify the Given Values:
- The probability of winning a game, [tex]\( P(\text{win}) \)[/tex], is 25% or 0.25.
- The total number of games played, [tex]\( n \)[/tex], is 20.
2. Understand the Concept of Expected Value:
- The expected number of wins ([tex]\( E(\text{wins}) \)[/tex]) can be calculated by multiplying the probability of winning one game by the total number of games played.
3. Apply the Formula for Expected Value:
- The formula to calculate the expected number of wins is:
[tex]\[
E(\text{wins}) = P(\text{win}) \times n
\][/tex]
- Substitute the given values into the formula:
[tex]\[
E(\text{wins}) = 0.25 \times 20
\][/tex]
4. Calculate the Expected Number of Wins:
- Perform the multiplication:
[tex]\[
0.25 \times 20 = 5
\][/tex]
### Conclusion:
- You should expect to win 5 times if you play the game 20 times.
Therefore, the correct answer is:
- 5 times
