Question

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)

Answer 1

Answer:

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