Question

Suppose George wins 34​% of all chess games. ​(a) What is the probability that George wins two chess games in a​ row? ​(b) What is the probability that George wins three chess games in a​ row? ​(c) When events are​ independent, their complements are independent as well. Use this result to determine the probability that George wins three chess games in a​ row, but does not win four in a row.

Answer 1

Answer:

a) There is a 11.56% probability that George wins two chess games in a​ row.

b) There is a 3.93% probability that George wins three chess games in a​ row.

c) There is a 2.6% probability that George wins three chess games in a​ row, but does not win four in a row.

Step-by-step explanation:

For each chess game that George plays, there is a 34% probability that he wins and a 100-34 = 66% probability that he loses.

(a) What is the probability that George wins two chess games in a​ row?

The are two games:

G1-G2

We want the following set of results:

W-W

A W has 34% probability.

So

$P = 0.34*0.34 = 0.1156$

There is a 11.56% probability that George wins two chess games in a​ row.

(b) What is the probability that George wins three chess games in a​ row?

The are three games:

G1-G2-G3

We want the following set of results:

W-W-W

A W has 34% probability.

So

$P = 0.34*0.34*0.34 = 0.0393$

There is a 3.93% probability that George wins three chess games in a​ row.

(c) When events are​ independent, their complements are independent as well. Use this result to determine the probability that George wins three chess games in a​ row, but does not win four in a row.

The are four games:

G1-G2-G3-G4

We want the following set of results:

W-W-W-L

A W has 34% probability. A L has 66% probability

So

$P = 0.34*0.34*0.34*0.66 = 0.026$

There is a 2.6% probability that George wins three chess games in a​ row, but does not win four in a row.

Answer 2

Answer:

Step-by-step explanation:

Probability of winning a game = 0.34

a) Probability of winning two games simultaneously = .34 x .34 =.1156

b) Probability of winning 3 games in a row = .34³

c) Probability of winning three chess games in a row and failure in the fourth = .34³ x ( 1-.34)

c)