A k out of n system is one in which there is a group of ncomponents, and the system will function if at least kof the components function. Assume the components function independently of one another. In a 3 out of 5 system, each component has a probability of 0.9 of functioning. What is the probability that system will function?

0.99145 is the probability that the system will work properly.

Step-by-step explanation:

We are given the following information:

The components function independently of one another.

We treat component working properly as a success.

P(component working properly) = 0.9

Then the number of components follows a binomial distribution, where

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 5 and x = 3

For the system to function if atleast 3 out of 5 will work properly.

We have to evaluate:

0.99145 is the probability that the system will work properly.

im not sure of the names, but the answer is 48