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.

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

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

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

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