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 0.09 0.5 0.01 _____

(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

Solution :

The total probability must be equal to one.

P(a) = 0.1, P(b) = 0.09, P(c) = 0.5, P(d) = 0.01

Hence, P(e) = 1 - (0.1 + 0.09 + 0.5 + 0.01)

P(e) = 0.3

Outcome	a	b	c	d	e
Probability	0.1	0.09	0.5	0.01	0.3

a) P({a, c, e}) = P(a).P(c).P(e)

P({a, c, e}) = 0.1 × 0.5 × 0.3

P({a, c, e}) = 0.015

b) E = {a, c, e} and F = {b, c, e} then we have to find P(E ∪ F)

(E ∪ F) = {a, b, c, e}

P(E ∪ F) = P({a, b, c, e})

P(E ∪ F) = 0.1 × 0.09 × 0.5 × 0.3

P(E ∪ F) = 0.00135

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

P(E') = 1 - P({a, c, e})

P(E') = 1 - (0.1 × 0.5 × 0.3)

P(E') = 1 - 0.015

P(E') = 0.985

d) E = {a, c, e} and F = {b, c, e} then we have to find P(E ∩ F)

(E ∩ F) = {c, e}

P(E ∩ F) = P({c, e})

P(E ∩ F) = 0.5 × 0.3

P(E ∩ F) = 0.15