Question

A probability experiment is conducted in which the sample space of the experiment is

Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSetS={7,8,9,10,11,12,13,14,15,16,17,18}.

Let event

Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSetE={7,8,9,10,11,12}.

Assume each outcome is equally likely. List the outcomes in

Upper E Superscript cEc.

Find

?P(Upper E Superscript cEc?).

The outcomes in

Upper E Superscript cEc

are

StartSet nothing EndSet{}.

?(Use a comma to separate answers as? needed.)

?P(Upper E Superscript cEc?)equals=nothing

?(Type an integer or a simplified? fraction.)

Answer 1

a) Eᶜ = {13,14,15,16,17,18}

The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

b) P(Eᶜ) = (1/2) = 0.5

P(Upper E Superscript c) = (1/2) equals 0.5

Explanation:

The set that represents the universal set with all the sample spaces is set S and is given by

Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

S = {7,8,9,10,11,12,13,14,15,16,17,18}

Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet

Event E = {7,8,9,10,11,12}

a) Find Eᶜ

Eᶜ is the complement of event E; it includes all the outcomes in the universal set, S, that are not in the event E

Eᶜ = {13,14,15,16,17,18}

The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

b) P(Upper E Superscript c) = P(Eᶜ)

= n(Eᶜ) ÷ n(S)

Each outcome is equally likely, hence,

n(Eᶜ) = number of outcomes in the event Eᶜ = 6

n(S) = number of outcomes in the set S = 12

P(Eᶜ) = (6/12) = (1/2) = 0.5

Hope this Helps!!!