Question

Based on the records for the past several​ seasons, a sports fan believes the probability the red team wins is 0.35. The fan also believes the probability the blue team wins is 0.40. In a season with 140 ​games, how many fewer games should the fan expect the red team to​ win?
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Part 1
The fan should expect the red team to win
  
enter your response here fewer games than the blue team.

Answer 1

To find out how many fewer games the red team should expect to win compared to the blue team, we can follow these steps:

1. **Calculate the expected wins for the red team:**
\[
\text{Expected Wins (Red Team)} = P(\text{Red Wins}) \times \text{Total Games}
\]
Substituting the values:
\[
\text{Expected Wins (Red Team)} = 0.35 \times 140 = 49
\]

2. **Calculate the expected wins for the blue team:**
\[
\text{Expected Wins (Blue Team)} = P(\text{Blue Wins}) \times \text{Total Games}
\]
Substituting the values:
\[
\text{Expected Wins (Blue Team)} = 0.40 \times 140 = 56
\]

3. **Determine how many fewer games the red team should expect to win compared to the blue team:**
\[
\text{Fewer Wins} = \text{Expected Wins (Blue Team)} - \text{Expected Wins (Red Team)}
\]
Substituting the values:
\[
\text{Fewer Wins} = 56 - 49 = 7
\]

Thus, the fan should expect the red team to win **7 fewer games** than the blue team.