Answer to Question #110194 in Statistics and Probability for Yusuf

Question

Let A represent the event that someone lives with ASD and B represent the event that someone does not live with ASD.
Question 23 Which of the following statements is correct?
(1) P(A and B) = P(A)* P(B)
(2) P(A|B) = P(A)
(3) P(B) ≠ P(Ac)
(4) Events A and B are mutually exclusive.
(5) Events A and B are independent.

Question 24 Suppose further that P(A) = 0.96 and P(B) = 0.04. P(A or B) = ??
(1) 0.92
(2) 0.0384
(3) 1
(4) 0.96
(5) 0.04

Answer 1

events,

 A : Someone lives with ASD 

B : Someone live without ASD

Question 23

There are no intercept between these two events.

$\therefore P(A\ and\ B)=\emptyset\\ Also,\ P(A|B)=\frac{P(A\ and\ B)}{P(B)}=\emptyset\\$

Therefore first two statements are wrong.

$P(A\cup B)=P(A)+P(B)\\ \therefore P(B)=1-P(A)=P(Ac)\\$

Therefore third statement is wrong.

If A is increased, then B is decreased vice versa. Therefore they are dependent and fifth statement is wrong.

since,

$P(A\cup B)=P(A)+P(B)\\$

A and B are mutually exclusive and statement (4) is correct.

Question 24

A and B are mutually exclusive and

$P(A\cup B)=P(A)+P(B)\\ P(A\cup B)=0.96+0.04\\ P(A\cup B)=1$

Therefore the answer is (3)