Probability: sudden death playoff Teams A and B go into sudden death overtime after playing to a tie. The teams alternate possession of the ball and the first team to score wins. Each team has a chance of scoring when it has the ball, with Team A having the ball first.

a. The probability that Team A ultimately wins is . Evaluate this series.

b. The expected number of rounds (possessions by either team) required for the overtime to end is . Evaluate this series.

Solution 70E

Step 1:

a. The probability that Team A ultimately wins is .This is the sum of an infinite geometric series whose first term and common ratio

Sum of an infinite geometric series is .Hence