# discrete probability distribution (help please!)

posted by .

a machine has 7 identical components which function independently. the probability that a component will fail is 0.2. the machine will stop working if more than three components fail. find the probability that the machine will be working.

• discrete probability distribution (help please!) -

Add the probabilities that 0, 1, 2 or 3 components have failed. That sum will be the probability that the machine works.

The probability that none have failed is
P(0) = 0.8^7 = 0.210

The probability that one part has failed is
P(1) = 0.8^6*0.2*7 = 0.367

The probability that two parts have failed is P(2) (0.8)^5*(0.2)^2*[7!/(5!2!)] = 0.275

The probability that three parts have failed is P(3) = (0.8)^4*(0.2)^30*[7!/4!3!)] = 0.115

The sum of these probabilities is 0.967.

• discrete probability distribution (help please!) -

thank you so very much! you're my hero! =D

## Similar Questions

1. ### Intro to Probability

Widgets are produced at a certain factory by each of three machines A, B and C. These machines produce 1000, 600 and 400 widgets per day, respectively. The probability that a given widget is defective is 4% for one produced by Machine …
2. ### math

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other …
3. ### stat

a machine has 7 identical components which function independently. the probability that a component will fail is 0.2. the machine will stop working if more than three components fail. find the probability that the machine will be working.
4. ### Elementary Statistics

A machine has 7 identical components which function independently. The probability that a component will fail is .2. The machine will stop working if more than three components fail. Find the probability that the machine will be working?
5. ### Math

A company that produces a particular machine component has 3 factories, one each in Buffalo, Detroit, and Pittsburgh. 39% of the components produced come from the Buffalo factory, 36% of the components come from the Detroit factory, …
6. ### Math

A company that produces a particular machine component has 3 factories, one each in Buffalo, Detroit, and Pittsburgh. 39% of the components produced come from the Buffalo factory, 36% of the components come from the Detroit factory, …
7. ### Maths

a missile guidance system has five fail-safe components. the probability of each failing is 0.05. find these probabilities. a) Exactly 2 will fail b) More than 2 will fail c) All will fail. d) Compare the answer for parts a, b, c, …
8. ### problem solving

for a parallel structure of identical components, the system can succeed if at least 1 of the components succeeds. Assume that components fail independently of each other and that each component has a 0.19 probability of failure. A) …
9. ### Statistics

A certain type of artificial heart has four independent, critical components.Failure of any one of these components is a serious problem that will cause the artificial heart to fail. The 5 year failure rate for each component follows: …
10. ### Math 141

Three machines turn out all the products in a factory, with the first machine producing 20% of the products, the second machine 15%, and the third machine 65%. The first machine produces defective products 17% of the time, the second …

More Similar Questions