Question

It is possible for a computer to pick up an erroneous signal that does not show up as an error on the screen. The error is called a silent paging error. A particular terminal is defective, and when using the system word processor, it introduces a silent paging error with probability 0.1. The word processor is used 20 times during a given week. (From Milton & Arnold 4th Edition, page 89)

What is the probability that at least 3 errors occur?

  

0.043

   

0.133

   

0.323

   

0.867

Answer 1

we have probability p = 0.10

sample size is n = 20

we have to find the probability of at least 3 error

we can write P(at least 3) = P(total) - P(0) - P(1) - P(2)

where P(0), P(1) and P(2) are probability of making of 0,1 and 2 errors respectively.

so, we need to find the value of P(0), P(1) and P(2) using the binomial distribution formula

we have the following formula

P(x=r) =

setting the values, we get

P(0) =

this gives us

P(0)= 0.1216

Again for P(1)

P(1) =

this gives us

P(1)= 0.2702

Similarly for P(2), we get

P(2) =

this gives us

P(2)= 0.2852

So, required probability P(at least 3) = P(total) - 0.1216-0.2702-0.2852 = 1 - 0.677 = 0.323

So, Required probability P(at least 3) = 0.323

OPTION C IS CORRECT ANSWER