Probability of Filling 100 Orders w/ Defective Components

[natethegreatX]

Homework Statement

A manufacturer has 100 customers and needs to make one component per customer. However 2% of the components manufactured come out defective. The components can be assumed to be independent.

If the manufacturer stocks 100 components, what is the probability that the 100 orders can be filled without re-ordering new components?

If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without re-ordering new components?

Homework Equations

Not sure, but possibly:

(n!)/(x!(n-x)!)*(p^x)(1-p)^(n-x)

p=probability of failure
n=number of tries
x=number of independent variable

The Attempt at a Solution

The only real problem I'm having is with this equation, the first question goes to 1, and the second goes to zero. I feel those arn't right at all. Wouldn't the first question end up 98%?
So I'm lost on if the binomial distribution function is even supposed to be used or if I just can't plug numers in a calc properly. Oh and this is my official first post on the forums.

 

[NeoDevin]

Please clarify that equation, what does it equal?

 

[dacruick]

if you don't mind telling me the "section" of probability that this question is under, I'm sure I could find an answer for you.

 

[dacruick]

okay what is the probability that a coin will be flipped 100 times, and there will be no heads. this is the same concept as the first question.

The second question is like, what is the probability that a coin is tossed 102 times, and there will be at least 100 heads. Or, in other words, what is the probability a coin is tossed and there are less than 3 tails.