Answer to Question #113684 in Statistics and Probability for Katenda

Question

Question 26

Consider the sample space S = {1, 2, 3, 4, 5} and let A be a set of numbers less or equal to 4 and B be set of numbers greater than 4. Both A and B are subsets of S.

Which one of the following statements is incorrect?

(1) A = {1, 2, 3, 4} and B = {5}
(2) P(A) = 4/5
(3) P(B) = 1/5
(4) Events A and B are mutually exclusive.
(5) Events A and B are independent.

Answer 1

$\text{If A and B are independent,this means that} \\ P(A\bigcap B)=P(A)\times P(B), but,\\ P(A)=\frac{4}{5},P(B)=\frac{1}{5}, \\ P(A\bigcap B)=0\neq P(A)\times P(B)\\ \text{so the incorrect statement is }\\ \text{(5) A and B are independent}$