# Probability Distribution

1. Dec 20, 2007

### kevykevy

1. The problem statement, all variables and given/known data

10% of the keyboards a computer company manufactures are defective. 3 keyboards come off the assembly line. Determine the probability distribution, where x=the number of defective keyboards. What would the expected number of defected keyboards be?

2. Relevant equations

I haven't done data management in over a year, this is the reason I can't do the question...I don't know what the equation is for probability distribution.

3. The attempt at a solution

After finding the probability distribution, I suppose I can just multiply it by 3?

2. Dec 21, 2007

### HallsofIvy

Staff Emeritus
There is no one probability distribution. What you want is the "binomial probability distribution". If, on each trial, an event happens with probability p, then the probability the event will happen i times in n trials is $P(i)= _nC_i p^i(1-p)^{n-i}$ where $_nC_i$ is the "binomial coefficient". Here, n= 3 and p= 0.10.

No, you cannot just multiply the probability distribution by 3. The expected value in 3 "trials" is 0P(0)+ 1P(1)+ 2P(2)+ 3P(3). That is, for i= 0, 1, 2, 3, you multiply the probability that many are faulty by the number, then add.

3. Dec 21, 2007

### nicksauce

Alternatively, you can just use the fact that for a binomial distribution with number N and probability P, the expected value is NP.