A brand name has a 40 recognition rate Assume the owner of t

A brand name has a 40% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 4 randomly selected consumers. (a) What is the probability that all of the selected consumers recognize the brand name? Please show the steps so I understand how to get the answer thanks!

Solution

n= 4

p = 0.4

x = 4

P(X=x) = (nCx)    p^x (1-p)^n-x   

P(X=4) = (4C4)   0.4 ^ 4   (1-0.4) ^ 4-4

P(X=4) = (1) (0.0256) (1)   

P(X=4) = 0.0256