Question

Complete the following probability distribution table and then calculate the stated probabilities. HINT [See Quick Example 5.]

Outcome	a	b	c	d	e
Probability	0.1	0.01	0.4	0.09

(a)    P({a, c, e})
P({a, c, e}) =

(b)    P(E ∪ F), where E = {a, c, e} and F = {b, c, e}
P(E ∪ F) =

(c)    P(E'), where E is as in part (b)
P(E') =

(d)    P(E ∩ F ), where E and F are as in part (b)
P(E ∩ F) =

Answer 1

a) The sum of all the probabilities would be 1. Hence,

0.1 + 0.01 + 0.4 + 0.09 + P(e) = 1

0.6 + P(e) = 1

P(e) = 0.4

Hence,

P({a, c, e}) = 0.1 + 0.4 + 0.4 = 0.9

b) P(E U F) = P(a, b, c , e) = 1 - P(d) = 1 - 0.09 = 0.91

c) P(E') = 1 - P(E) = 1 - 0.9 = 0.1

d) P(E F) = P(c, e) = 0.4 + 0.4 = 0.8