Question 243421
ok. if i have an eighty percent chance of selecting the right outcome for a particular event, then i know the probability for selecting the right outcome for four, five or six events in a row. but what is the probability of selecting the right outcome four out of six times, or five out of six times. I'm getting a little confused when the outcomes are not in a row. Because four out of six could be four hits in a row or it could be miss,hit,hit,hit,miss,hit and so on. please help. thanks, tim
---------------------
Everything you said is correct.
"But what is the probability of selecting the right outcome four out of six times, or five out of six times."
----
Four out of six:
The prob of rrrrww is (0.8)^4(0.2)^2
And prob of rrrwwr is (0.8)^4(0.2)^2
And there are 6C4 = 6C2 = 15 of these patterns.
Each of the patterns has the same probability 
and they are all mutually exclusive (that means
if you get one of the patterns you cannot simultaneously
get another one of the patterns).
So you add all those equal probabilities and get
15*0.8^4*0.2^2 = 0.24576....
---------------------------------
Five out of six:
The prob of 5 out of six follows the same logic:
rrrrrw has the same probability as rrrrwr and 
there are 6C5=6C1=6 such patterns.
Each pattern has prob = (0.8)^5*(0.2)^1
---
So the prob of 5 out of 6 is 6C5*0.8^5*0.2 = 0.3932...
---------------
In general P(r successes in n trials) = nCr*p^r*q^(n-r)
===========================================================
Cheers,
Stan H.