stats hw help..

Question

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

Sequals=StartSet 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 EndSet{4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}​,

event

Upper F equals StartSet 5 comma 6 comma 7 comma 8 comma 9 comma 10 EndSetF={5, 6, 7, 8, 9, 10}​,

and event

Upper G equals StartSet 9 comma 10 comma 11 comma 12 EndSetG={9, 10, 11, 12}.

Assume that each outcome is equally likely. List the outcomes in F or G. Find

Upper P left parenthesis Upper F or Upper G right parenthesisP(F or G)

by counting the number of outcomes in F or G. Determine

Upper P left parenthesis Upper F or Upper G right parenthesisP(F or G)

using the general addition rule.

List the outcomes in F or G. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

                                               

Answer 1

The formatting of this question is a bit awkward. I hope I understand the problem correctly.

I looks like we have a sample space S = {4, 5, 6, ..., 15}

And two subsets F = {5, 6, 7, 8, 9, 10} and G = {9, 10, 11, 12}

And we are asked to determine the Probability of {F or G}, assuming all events are equally likely.

What is the set {F or G}? It is the set of all elements in either F or G

{5, 6, 7, 8, 9, 10, 11, 12} Note: we do not repeat elements in both F and G.

How many elements are in the subset {F or G}?

How many elements are there in the sample space?

Probability(F or G)= # elements in the subset {F or G} / # elements in the sample space.

Prob(F or G) = 8/12 = 2/3

Think of this as a game of chance. Imagine a televised 'Lotto' with ping pong balls numbered 4 through 15 bouncing around in chamber, and one of the balls will pop out of the chamber, and that ball will be the winner. (We are assuming that this is a "fair" lottery, and each ball has the same chance of being selected.) What are the chances that the winning ball is either the ball numbered 5, 6, 7, ..., or 12?

The chances are 8 out of 12, right? Simple as that!

But a probability is a number between 0 and 1, expressed as a fraction or a decimal. So we don't say the chances are "8 out of 12", we say the probability is 8/12 = 2/3 = 0.67

Hope that makes sense.

Once you get the hang of it, probability is super fun!