Question

In a certain diagnostic test, there is a 0.025% chance of a false result. If 10,000 units were administered this test, what is the probability that exactly 1 unit will produce a false result?

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.00025

N = number of trials = 10,000

R = desired success = 1

P(1) = 10000c1*(0.00025^1)*(1-0.00025)^10,000-1 = 0.2051996669