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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.

1 answer

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.