What is the Expected Number of Defective Keyboards?

[kevykevy]

Homework Statement

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?

Homework 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.

The Attempt at a Solution

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

 

[HallsofIvy]

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.

 

[nicksauce]

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