Question

Suppose that the Raptors have an approximate 45% chance of winning against the Golden State Warriors (San Francisco’s basketball team) in any one game, and that the outcomes of each game are independent of others. In the NBA finals, the first team to win four out of seven games will win the championships. Once four games are won, the championships are over and any remaining games will not be played.

Find the probability that the Raptors win the NBA finals against the Golden State Warriors, if the winner is determined as the team that is first to win four out of seven games

Answer 1

Let X be the number of games played till any team win four out of seven games. The values of X will be 4, 5, 6, 7.

For X = 4,

Probability that the Raptors win a NBA finals = Probability that the Raptors wins all first four games = 0.45⁴ = 0.04100625

For X = 5,

Probability that the Raptors win a NBA finals = Probability that the Raptors wins three games of first four games and wins fifth game = ⁴C₃ * 0.45³ * (1 - 0.45) * 0.45 = 4 * 0.45⁴ * 0.55 = 0.09021375

For X = 6,

Probability that the Raptors win a NBA finals = Probability that the Raptors wins three games of first five games and wins sixth game = ⁵C₃ * 0.45³ * (1 - 0.45)² * 0.45 = 10 * 0.45⁴ * 0.55² = 0.1240439

For X = 7,

Probability that the Raptors win a NBA finals = Probability that the Raptors wins three games of first six games and wins seventh game = ⁶C₃ * 0.45³ * (1 - 0.45)³ * 0.45 = 20 * 0.45⁴ * 0.55³ = 0.1364483

Probability that the Raptors win a NBA finals = 0.04100625 + 0.09021375 + 0.1240439 + 0.1364483

= 0.3917122