Suppose % of all . (a) What is the probability that two in a row? (b) What is the probability that in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that in a row, but in a row. (a) The probability that two in a row is . 1156. (Round to four decimal places as needed.) (b) The probability that in a row is . 0393. (Round to four decimal places as needed.) (c) The probability that in a row, but in a row is

(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:

(a) [tex]Probability = 0.1156[/tex]

(b) [tex]Probability = 0.0393[/tex]

(c) [tex]Probability = 0.0259[/tex]

Step-by-step explanation:

Represent Win with W

So, we have:

[tex]W = 34\%[/tex]

Solving (a): Winning two in a row;

This is represented by WW and is calculated as thus:

[tex]Probability = W * W[/tex]

[tex]Probability = 34\% * 34\%[/tex]

[tex]Probability = 0.1156[/tex]

Solving (b): Winning three in a row;

This is represented by WWW and is calculated as thus:

[tex]Probability = W * W * W[/tex]

[tex]Probability = 34\% * 34\% * 34\%[/tex]

[tex]Probability = 0.039304[/tex]

[tex]Probability = 0.0393[/tex] (Approximated)

Solving (c): Wins three in a row but lost the fourth

Represent Losing with L

L is calculated as:

[tex]L = 1 - W[/tex] ---- Complement of probability

[tex]L = 1 - 34\%[/tex]

[tex]L = 66\%[/tex]

This probability is represented by WWWL and is calculated as thus:

[tex]Probability = 34\% *34\% *34\% *66\%[/tex]

[tex]Probability = 0.02594064[/tex]

[tex]Probability = 0.0259[/tex] (Approximated)