Suppose three players go on multiple rounds of kart race. In each round, every player has a winning probability of 1/3, independent of other rounds. Let N denote the number of rounds until player 1 has two consecutive wins.

a) Find P (N < = 10)

b) Find P (N = 10)

Question

Jonathan Cantrell

Mathematics

21 October, 08:02

Suppose three players go on multiple rounds of kart race. In each round, every player has a winning probability of 1/3, independent of other rounds. Let N denote the number of rounds until player 1 has two consecutive wins.

a) Find P (N < = 10)

b) Find P (N = 10)

+4

Answers (1)

Know the Answer?

Margaret Gentry · Answer 1

a) 0.3246

b) 0.0043

Step-by-step explanation:

For player 1; Probability of winning = P (W) = 1/3 Probability of loosing; P (winning) + P (Loosing) = 1 P (L) = 1 - 1/3 = 2/3

a) To find Find P (N < = 10) = P (2) + P (3) + P (4) + P (5) + P (6) + P (7) + P (8) + P (9) + P (10)

= (1/3) ^2 + (1/3) ^2 x 2/3 + (1/3) ^2 x (2/3) ^2 + (1/3) ^2x (2/3) ^3 + (1/3) ^2 x (2/3) ^4

X (1/3) ^2 x (2/3) ^5 + (1/3) ^2 x (2/3) ^6 + (1/3) ^2 x (2/3) ^7 + (1/3) ^2 x (2/3) ^8

= 0.3246

b) Find P (N = 10) = (1/3) ^2 x (2/3) ^8 = 0.0043

Suppose three players go on multiple rounds of kart race. In each round, every player has a winning probability of 1/3, independent of other rounds. Let N denote the number of rounds until player 1 has two consecutive wins.a) Find P (N < = 10)b) Find P (N = 10)

Suppose three players go on multiple rounds of kart race. In each round, every player has a winning probability of 1/3, independent of other rounds. Let N denote the number of rounds until player 1 has two consecutive wins.

a) Find P (N < = 10)

b) Find P (N = 10)