Question

Question 2 (26 points) In an NBA (National Basketball Association) series, the team that wins four games out of seven is the winner and it will win the big prize. Suppose that teams A and B face each other in the games and that team A has probability 0.4 of winning a game over team B. a) (13 points) Compute the probability that team A wins the big prize at (just after) the 6"game. b) (13 points) Compute the probability that team A wins the big prize?

Answer 1

2.

P(X) = nCx p*(1-p)*-*

x = no. of A wins

p = 0.4

1-p = 0.6

a.

P(A wins at 6th game)

= P(3 wins in 5 games)*P(win in 6th game)

= (5C3 * 0.4^3 * 0.6^2) * 0.4

= (10 * 0.4^3 * 0.6^2) * 0.4

= 0.09216

b.

P(A wins)

= P(A wins 4 or more out of 7)

= (7C4 * 0.4^4 * 0.6^3) + (7C5 * 0.4^5 * 0.6^2) + (7C6 * 0.4^6 * 0.6^1) + (7C7 * 0.4^7 * 0.6^0)

= (35 * 0.4^4 * 0.6^3) + (21 * 0.4^5 * 0.6^2) + (7 * 0.4^6 * 0.6^1) + (1 * 0.4^7 * 0.6^0)

= 0.289792

(please UPOTE)