Question

A team that wins 4 games out of 7 is the winner. Suppose that Team S and Team R face each other in the final game and that Team S has probability 0.55 of winning a single game over Team R . Find:

The probability that Team S will win the series.

Answer 1

P[ team S wins the game ] = p = 0.55

P[ team S losses the game ] = 1 - P[ team S wins the game ] = q = 1 - 0.55 = 0.45

A team that wins 4 games out of 7 is the winner.

X be the number of games S wins

X~B(7,0.55) ( each game is independent and probability remain same for each wining )

P[ Team S will win the series ] = P[ X >= 4 ]

P[ X >= 4 ] = P[ X = 4 ] + P[ X = 5 ] + P[ X = 6 ] + P[ X = 7 ]

P[ X= k ] = nCk*p^k*q^(n-k)

P[ X = 4 ] = 7C4*0.55^4*0.45^3 = 0.2918

P[ X = 5 ] = 7C5*0.55^5*0.45^2 = 0.2140

P[ X = 6 ] = 7C6*0.55^6*0.45^1 = 0.0872

P[ X = 7 ] = 7C7*0.55^7*0.45^0 = 0.0152

P[ X >= 4 ] = 0.2918 + 0.2140 + 0.0872 + 0.0152

P[ X >= 4 ] =0.6082

P[ Team S will win the series ] = P[ X >= 4 ] = 0.6082