Respuesta :
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
[tex]P = 0.34*0.34 = 0.1156[/tex]
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
[tex]P = 0.34*0.34*0.34 = 0.0393[/tex]
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
[tex]P = 0.34*0.34*0.34*0.66 = 0.026[/tex]
There is a 2.6% probability that George wins three chess games in a row, but does not win four in a row.
