The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2, respectively. Let A denote the event {a, b, c}, and let B denote the event {c, d, e}. Determine the following:

(a) P (A)

(b) P (B)

(c) P (A')

(d) P (AUB)

(e) P (AnB)

a) 0.4

b) 0.8

c) 0.6

d) 1

e) 0.2

Step-by-step explanation:

a) P (A) = P ({a, b, c}) = 0.1 + 0.1 + 0.2 = 0.4

b) P (B) = P ({c, d, e}) = 0.2 + 0.4 + 0.2 = 0.8

c) P (A') = 1 - P (A) = 1 - 0.4 = 0.6

d) P (AUB) = P ({a, b, c}U{c, d, e}) = P ({a, b, c, d, e}) = 0.1 + 0.1 + 0.2 + 0.4 + 0.2 = 1

e) P (AnB) = P ({a, b, c}n{c, d, e}) = P ({e}) = 0.2