Given the following information about events A, B and C determine which pairs of events, if any, are independent and which are mutually exclusive. P(A) = 0.26, P(A|B) = 0.26, P(B) = 0.5, P(B|C) = 0, P(C)=0.45, P(C|A) =0.26.

Select all that apply:

a. Are B and C independent?
b. Are A and C mutually exclusive?
c. Are A and B independent?
d. Are A and B mutually exclusive?

a. Are B and C independent?    NO

b. Are A and C mutually exclusive?   NO

c. Are A and B independent?    YES

d. Are A and B mutually exclusive?  NO

Step-by-step explanation:

Given the data in the question;

P(A|B) = 0.26 P(A)   [ A and B are independent ]

P(B|C) = 0          [ B and C are mutually exclusive ]

P(C/A) = 0.26 ≠ P(C)

hence, [A and C are neither independent nor mutually Exclusive]

Therefore;

a. Are B and C independent?    NO

b. Are A and C mutually exclusive?   NO

c. Are A and B independent?    YES

d. Are A and B mutually exclusive?  NO

-14

step-by-step explanation:

2x2 – 2(x+4)

=2x2-2（5+4）

=4-2×9

=4-18

=-14