If the probability is 01 that a person will make a mistake o

If the probability is 0.1 that a person will make a mistake on his or her state income tax return, find the probability that (a) four totally unrelated persons each make a mistake; (b) Mr. Jones and Ms. Clark both make mistakes, and Mr. Roberts and Ms. Williams do not make a mistake.

Solution

P(person makes a mistake) =0.1

P(person doesn\'t make mistake) = 1 - 0.1 = 0.9

(a) Since the events are independent,

P(ABCD) = P(A)*P(B)*P(C)*P(D).

P(ABCD) = (.1)(.1)(.1)(.1) = 0.0001

(b)

P(ABCD) = P(A)*P(B)*P(C)*P(D).

P(ABCD) = 0.1*0.1*0.9*0.9 = 0.0081