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The Cubs are playing the Red Sox in the World Series. To win the world series, a team must win 4 games before the other team does. If the Cubs win each game with probability \(\frac35\) and there are no ties, what is the probability that the Cubs will win the World Series? Express your answer as a percent rounded to the nearest whole percent.

 Mar 8, 2019

\(P[\text{Cubs win the series}] = \sum \limits_{l=0}^3~\left(\dfrac 3 5\right)^4 \left(\dfrac 2 5\right)^l = \dfrac{16443}{78125} \approx 0.21 = 21\%\)

 Mar 8, 2019

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