Question

Please help me!
2. What must be true in order for P (A or B) = P(A) + P (B)? (1 point)
A.A and B cannot be disjoint.
B.A and B must be independent.
C.A and B cannot be independent.
D.A and B must be disjoint.
E.It is always true.
3. What must be true for P (A and B) = P (A) • P (B)? (1 point)
A.A and B cannot be independent.
B.A and B must be disjoint.
C.A and B must be independent.
D.A and B cannot be disjoint.
E.It is always true.

Answer 1

(2)

we are given

P(A or B)=P(A)+P(B)

we know formula is

P(A or B) = P(A)+P(B)-P(A∩B)

now, if A and B are  disjoint

so,

P(A∩B) =0

now, we can plug it

P(A or B) = P(A)+P(B)-0

P(A or B) = P(A)+P(B)

so, option-D...........Answer

(3)

P (A and B) = P (A) • P (B)

we know that

If A and B are independent events

then

P (A and B) = P (A) • P (B)

so, option-C...........Answer