Question

a probability experiment is conducted in which the sample space of the experiment is s = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, event f = {3, 4, 5, 6, 7, 8}, and g = {7, 8, 9, 10}. 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.
list the outcomes in f or g. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. f or g = {3,4,5,6,7,8,9,10}
(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) =
(type an integer or a decimal rounded to three decimal places as needed.)

Explanation:

Step1: Determine total number of outcomes in sample space

The sample space $S = \{1,2,3,4,5,6,7,8,9,10,11,12\}$, so $n(S)=12$.

Step2: Count number of outcomes in F or G

We know $F\ or\ G=\{3,4,5,6,7,8,9,10\}$, so $n(F\ or\ G) = 8$.

Step3: Calculate probability

The probability formula is $P(A)=\frac{n(A)}{n(S)}$. Here $A = F\ or\ G$, so $P(F\ or\ G)=\frac{n(F\ or\ G)}{n(S)}=\frac{8}{12}=\frac{2}{3}\approx0.667$.

Answer:

$0.667$