Question

a probability experiment is conducted in which the sample space of the experiment is s = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, and f = {9, 10, 11, 12, 13, 14}, and event g = {13, 14, 15, 16}. assume that each outcome is equally likely. list the outcomes in f or g. find p(f or g) by counting the number of outcomes in f or g. determine p(f or g) using the general addition rule.

a. f or g = {9,10,11,12,13,14,15,16}
(use a comma to separate answers as needed.)
b. f or g = ()
find p(f or g) by counting the number of outcomes in f or g.
p(f or g) = 0.667
(type an integer or a decimal rounded to three decimal places as needed.)
determine p(f or g) using the general addition rule. select the correct choice below and fill in any answer boxes within your choice.
(type the terms of your expression in the same order as they appear in the original expression. round to three decimal places as needed.)
a. p(f or g) = + - =

b. p(f or g) = + =

Explanation:

Step1: Identify the number of elements in sets

The sample - space $S=\{9,10,11,12,13,14,15,16,17,18,19,20\}$, so $n(S) = 12$. The set $F=\{9,10,11,12,13,14\}$, so $n(F)=6$. The set $G = \{13,14,15,16\}$, so $n(G)=4$. The intersection $F\cap G=\{13,14\}$, so $n(F\cap G)=2$.

Step2: Use the general addition rule

The general addition rule for probability is $P(F\cup G)=P(F)+P(G)-P(F\cap G)$. Since each outcome is equally - likely, $P(F)=\frac{n(F)}{n(S)}$, $P(G)=\frac{n(G)}{n(S)}$, and $P(F\cap G)=\frac{n(F\cap G)}{n(S)}$.
$P(F)=\frac{6}{12}=0.5$, $P(G)=\frac{4}{12}\approx0.333$, $P(F\cap G)=\frac{2}{12}\approx0.167$.
$P(F\cup G)=\frac{6}{12}+\frac{4}{12}-\frac{2}{12}=\frac{6 + 4-2}{12}=\frac{8}{12}\approx0.667$.

Answer:

A. $P(F\text{ or }G)=\frac{6}{12}+\frac{4}{12}-\frac{2}{12}=0.667$