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
You are talking about binomial probabilities.
It doesn't matter whether the right outcomes are in a row or not.
If the probability of 1 success in 1 trial is p, then the probability
of exactly x successes in n trials (regardless of the order in which
the successes occur) is given by this formula:
Sometimes is written and sometimes
it's written . Sometimes it is called
"n choose x" and sometimes "the combinations of n things
taken x at a time", and sometimes "the n,x binomial coefficient".
But however it's written and whatever
it's called it means or
In your problem, the probability of getting exactly 4 successes
out of 6 trials, when the probability of exactly 1 success in 1
trial is .8 can be gotten this way:
n = 6, p = .8, x = 4
In your other problem, the probability of getting exactly 5 successes
out of 6 trials, when the probability of exactly 1 success in 1
trial is .8 can be gotten this way:
n=6, p = .5, x = 5
You can also use a TI-84 calculator to find this
Press CLEAR
Press 2nd
Press VARS
Press ALPHA
Press MATH
You will see this on the screen:
binompdf(
type this 6,.8,4) after it and you will have this on the screen:
binompdf(6,.8,4)
Press ENTER
Read .24576
---------------
For the other one replace the 4 with a 5, and
you'll read .393216
Edwin