Question

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.
Assume the events are independent.

Answer 1

Answer: a) 0.0001, b) 0.0081.

Step-by-step explanation:

Since we have given that

Probability that a person will make a mistake on their state income tax return = 0.1

Probability that a person will not make any mistake = $1-0.1=0.9$

Since the events are independent.

So, (a) four totally unrelated persons each make a mistake;

Our probability becomes,

$P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)\\\\=0.1\times 0.1\times 0.1\times 0.1\\\\=0.0001$

(b) Mr. Jones and Ms. Clark both make mistakes, and Mr. Roberts and Ms. Williams do not make a mistake.

So, our probability becomes,

$P(A\cap B\cap C'\cap D')=P(A)\times P(B)\times P(C')\times P(D')\\\\=0.1\times 0.1\times 0.9\times 0.9\\\\=0.0081$

Hence, a) 0.0001, b) 0.0081.