A machine has 7 identical independent components.

Question

he probability that a component fails is .2. In order for the machine to operate, at least 6 of its 7 components must work. Find the probability that the machine fails.

Answer 1

Number of components (n) = 7

Probability of component fail (q) = 0.2

Probability of component works (p) = 1-q = 1 - 0.2 = 0.8

Number of components must work in order to operate machine (r) = 6

Using Binomial Probability , the Probability of machine operates = 

                                                                                           

                                                                                            = 7×0.2621×0.2

                                                                                            =0.367

The Probability of machine fails = 1 -  the Probability of machine operates

                                             = 1 - 0.367

                                             = 0.6329

Comments

please check the KLECK's answer for right answer

Answer 2

the machine operates if 6 or 7 of the components work, it fails if less than 6 work

let x = number of components that work

P(x = 6) = 7C6 * .8^6 * .2

P(x = 7) = 7C7 * .8^7

....................................

P(x < 6) = 1 - (7C6 * .8^6 * .2 + 7C7 * .8^7)

P(x < 6) = 1 - .5767168

P(x < 6) = .4232832

P(x < 6) = 42.33%

Comments

Thanks for correcting my mistake