During the 2018 season, the Chicago Cubs won 58% of their games. Assuming game outcomes are independent and the win percentage remains the same for this season, answer the following:
b. What is the probability that the Cubs will win seven consecutive games?

Verified step by step guidance

1. Identify the probability of the Cubs winning a single game, which is given as 58%, or 0.58 in decimal form.
2. Understand that the problem asks for the probability of winning seven consecutive games, which means winning game 1 AND game 2 AND ... AND game 7.
3. Since the outcomes are independent, the probability of winning seven consecutive games is the product of the probabilities of winning each individual game.
4. Write the expression for the probability of seven consecutive wins as \$0.58^{7}$, which means raising 0.58 to the power of 7.
5. Calculate \$0.58^{7}$ to find the probability of the Cubs winning seven games in a row.

Key Concepts

Probability of Independent Events

When events are independent, the outcome of one event does not affect the others. The probability of multiple independent events all occurring is the product of their individual probabilities. For example, the chance of winning seven games in a row is the product of the probability of winning each game.

Multiplication Rule for Probability

The multiplication rule states that to find the probability of several independent events happening together, multiply their individual probabilities. In this case, since each game win has a probability of 0.58, the probability of seven consecutive wins is 0.58 raised to the power of 7.

Interpreting Win Percentage as Probability

A team's win percentage can be interpreted as the probability of winning a single game if conditions remain consistent. Here, the 58% win rate means the probability of winning any given game is 0.58, which is used to calculate probabilities of sequences of wins.