SOLUTION: A computer has 100 components. The probability that a component will fail is 0.0022. Assuming that the components function independently, what is the probability that between 1 and

Algebra ->  Probability-and-statistics -> SOLUTION: A computer has 100 components. The probability that a component will fail is 0.0022. Assuming that the components function independently, what is the probability that between 1 and      Log On


   



Question 1001229: A computer has 100 components. The probability that a component will fail is 0.0022. Assuming that the components function independently, what is the probability that between 1 and 3 components will fail??
Confused as to how to even start this question. An explanation of the solution would be greatly appreciated!

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The probability of failure can be modeled as a function of the number of components that fail,
P%28x%29=C%28100%2Cx%29%2A%281-0.0022%29%5E%28100-x%29%280.0022%29%5E%28x%29
So for between 1 and 3 components failing calculate P%281%29, P%282%29, and P%283%29 and sum the probabilities.
C%28100%2C1%29=100
C%28100%2C2%29=4950
C%28100%2C3%29=161700
.
.
.
P%281%29=+100%2A%280.9978%29%5E99%2A%280.0022%29%5E1+=0.1769
P%282%29=+4950%2A%280.9978%29%5E98%2A%280.0022%29%5E2+=0.01931
P%283%29=+161700%2A%280.9978%29%5E97%2A%280.0022%29%5E3+=0.001391
So then,
P=0.1769%2B0.01931%2B0.001391
P=0.1976