Multiple Percentages Probability

[PharaohsVizier]

Hi, I seem to be having problems calculating this out. My friends were asking me how to caculate multiple precentages and I thought it would be easy but I got a little stuck. Here is the problem.

Lets say there is a program that spits out the words yes and no. 60% chance it says yes and 40% chance it says no. If I hit it once, there is a 60% chance it says yes and a 40% chance it says no. If I click it 7 times and it says yes 6 times, what are the odds? I put .6^6 to calculate it, but it seems that I don't include the fact that it says no once. Also, what would the odds be if it said yes all 7 times or no all 7 times? How would you calculate these percentages?

Thanks a lot, seems like a great forum so far.

 

[CRGreathouse]

You're looking for what's called the binomial distribution.

The odds of exactly 6 out 7 "yes" is (7 choose 6) * 0.6^6 * 0.4 ^ 1. Let me explain. You are getting 6 "yes" and 1 "no"; the chances of getting those answers []in that order[/i] is 0.6^6 * 0.4 ^ 1. Since you don't care about the order, you need to multiply this by the number of ways to choose 6 elements out of 7. In general, (x choose y) is

$$\frac{x!}{y!(x-y)!}$$

For (7 choose 6), that's 7!/(6! * 1!) = 7, giving a total probability of $7\cdot0.6^6\cdot0.4^1$.

 

[PharaohsVizier]

Thanks so much
I can't believe someone actually solved this for me in such a clear manner.
This forum is great!

 

[CRGreathouse]

Thanks so much
I can't believe someone actually solved this for me in such a clear manner.
This forum is great!

I'm glad to have helped.