Success rates

[melton]

hi guys, i dont even know if this question fits into this thread, so please excuse me if i am wrong. I have simple (i hope) question for most of you, but i cant even think about how to answer it.

if there is a piece of timber, and there are 6 screws in it, and each screw has a 5% chance of breaking when getting drilled in, what would would the failure rate of having 2 screws out of the 6 break?

can you please show me the formula and how to work it out so i can work it out with different numbers (i.e 1 screw fails, 2 screws out of the 6 fails, 3 screws out of the 6 fails, etc)

thanks.

 

[tkhunny]

What do you know of the Binomial Distribution? It will help you on your way.

Before you get too far, though, you should make SURE you know EXACTLY what "2 screws out of 6" means. Does it mean EXACTLY 2 or does it mean AT LEAST 2? In your case, since you are interested in all the values separately, it seems to mean EXACTLY. Just keep this kind of question in mind in order to avoid confusion.

 

[melton]

hi. thanks for the response.
im no maths student, and this isnt homework, and i have no idea what Binomial Distribution is, hence i am asking for the workings.

when i say 2 out of the 6, i mean exactly 2.

maybe i will reword my question.

6 screws at put in a piece of timber. whats the probability of 1 exactly failing, probability of 2 failing, etc etc,
When each screw is placed individually, it has a 5% chance of failure.

hope this helps.

 

[tkhunny]

There are a few ways to go about it. Sometimes, if the number is small enough, I'll just build a table:

All the failure possibilities are 0,1,2,3,4,5,6

Probability that One Fails = 0.05
Probability of Avoiding that Failure = 1 - 0.05 = 0.95
You should be able to see the pattern.

Then, just a little algebra:
0 - (1) (0.05)^0 (0.95)^6
1 - (6) (0.05)^1 (0.95)^5
2 - (15) (0.05)^2 (0.95)^4
3 - (20) (0.05)^3 (0.95)^3
4 - (15) (0.05)^4 (0.95)^2
5 - (6) (0.05)^5 (0.95)^1
6 - (1) (0.05)^6 (0.95)^0

That first number in each calculation (1, 6, 15, 20, etc.) is called a Binomial Coefficient. You can read up on that and inform your process.