Question

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

Answer 1

Complete 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:

(a) $Probability = 0.1156$

(b) $Probability = 0.0393$

(c) $Probability = 0.0259$

Step-by-step explanation:

Represent Win with W

So, we have:

$W = 34\%$

Solving (a): Winning two in a row;

This is represented by WW and is calculated as thus:

$Probability = W * W$

$Probability = 34\% * 34\%$

$Probability = 0.1156$

Solving (b): Winning three in a row;

This is represented by WWW and is calculated as thus:

$Probability = W * W * W$

$Probability = 34\% * 34\% * 34\%$

$Probability = 0.039304$

$Probability = 0.0393$ (Approximated)

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

Represent Losing with L

L is calculated as:

$L = 1 - W$ ---- Complement of probability

$L = 1 - 34\%$

$L = 66\%$

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

$Probability = 34\% *34\% *34\% *66\%$

$Probability = 0.02594064$

$Probability = 0.0259$ (Approximated)