Question

Please help! Probability Question.
If A an B are two events with sample points drawn from the same sample space. P(A) = .4 and P(B) = .5
Is it possible that A and B are mutually exclusive?
Is it possible that A and B are not mutually exclusive?
Is it possible that A and B are complementary.
Is it possible that A and B are not complementary?
Use the sample space in problem 1 to give examples to support your answers.

(1. Problem 1 sample space: They are a, b, c, d ,e f ,g ,h i, j, k, l, m, n, o, p, q, r, s, t.)

Answer 1

idk about the mutually exclusive part, but two events A and B are complementary if and only if

P(A) + P(B) = 1

Answer 2

Is it possible that A and B are mutually exclusive?
yes, it is possible since \(.4+.5=.9\) and \(.9<1\)

Answer 3

Is it possible that A and B are not mutually exclusive?
sure why not?

Answer 4

Is it possible that A and B are complementary.
no because of what @jim_thompson5910 said, the probabilities do not add to one