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Wewaii [24]
3 years ago
11

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.
Mathematics
2 answers:
Svetradugi [14.3K]3 years ago
7 0

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.

Sonbull [250]3 years ago
4 0

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)

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