HSC 96 q21d help please (1 Viewer)

[= Jennifer =]

peter has an 80% chance of winning each game of chess he plays in a particular competition. he is to play three games. he must win at least two of these games to make a final play off.

by using a tree diagram, or otherwise, find the probability that he makes the final play off.


can some one out there help me out?? thanks

 

[Demandred]

Something should come up like this:

win win win = .512
win win lose = .128
win lose win = .128
win lose lose = .032
lose win win = .128
lose win lose = .032
lose lose win = .032
lose lose lose = .008

To get those figures, you times the probability of one event to the next event, so e.g. win win win - .8 x .8 x .8 = .512

All of them should add to one if you did the calculations right.

Then add up all the outcomes where which he won twice or more. So:

.512 + .128 + .128 + .128 = .896

= 89.6% of making it to the playoffs.