1. (Tree Diagrams) Wayne and Kai keep playing chess until one of them wins two g
ID: 3302969 • Letter: 1
Question
1. (Tree Diagrams) Wayne and Kai keep playing chess until one of them wins two games in a row or one of them wins three games (not necessarily in a row). (a) In what percentage of all possible cases does the game end because Wayne wins three games without winning two in a row? (b) Supposing Wayne and Kai are equally skilled at chess, so that the probability of one of them winning a particular game is 0.5. What is the probability that the game ends because Wayne wins three games without winning two in a row? (Note that the answer to the two questions is not the same: (a) asks for the percentage of all outcomes, as if all outcomes are all equally likely; but in fact in (b) they are NOT equally likely, so you'll need to attach probabilities to the branches. Do the best you can to show this tree, it doesn't have to be pretty, just clear; and then give the answer to the questions.)Explanation / Answer
a)let winnning of Wayne and Kai are represented by W and K respectively,
therefore total possiblr outcomes: {WW,WKWW,WKWKW.KWW,KWKWW,KK.KWKK,KWKWK,WKK,WKWKK} =10
number of outcome in Wayne wins three games without winning two in a row =1
hence % of such games =(1/10)*100 =10%
b)probability that Wayne wins 3 games without winning two in a row =P(WKWKW)
=0.5*0.5*0.5*0.5*0.5=0.03125
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