Answer to Question #205677 in Statistics and Probability for Weam

Question

Let A and B be disjoint events and assume that Pr(A) = Pr(B) and Pr(AUB) = 0.8. Then Pr(A) =

Select one:

a. 0.4

b. 0.1

c. 0.2

d. 0.3

Answer 1

If two events $A$  and $B$ are disjoint, then

$$Pr(A \cup B) = Pr(A) + Pr(B).$$

Hence

$$Pr(A)=Pr(A \cup B)- Pr(B)$$

Given $Pr(A)=Pr(B)$

$$Pr(A)=Pr(A \cup B)- Pr(A)$$

$$Pr(A)=0.5Pr(A \cup B)$$

$$Pr(A)=0.5(0.8)=0.4$$

a. 0.4