# Probabiity two components are unacceptable

• Sep 19th 2013, 12:02 PM
mark090480
Probabiity two components are unacceptable
The probability that a chip is manufactured to an acceptable standard is 0.73. A sample of 4 chips is picked at random from a large batch.

I have calculated that all are acceptable 0.73^4 and none are 0.27^4. How can I calculate more than two are?

I tried 0.73^2 but then that + 0.27^2 does not make 1. What to do?

Thanks.
• Sep 19th 2013, 12:18 PM
Plato
Re: Probabiity two components are unacceptable
Quote:

Originally Posted by mark090480
The probability that a chip is manufactured to an acceptable standard is 0.73. A sample of 4 chips is picked at random from a large batch.
I have calculated that all are acceptable 0.73^4 and none are 0.27^4. How can I calculate more than two are?

$\sum\limits_{k = 3}^4 {\binom{4}{k}{{(.73)}^k}{{(.27)}^{4 - k}}}$
• Sep 19th 2013, 01:20 PM
HallsofIvy
Re: Probabiity two components are unacceptable
In other words, $4(.73)^3(.27)+ (.73)^4$!