Solution:
As given , Spinner has two equal Sections, one green and one Orange.
When the Spinner is Spun three times
Total Sample Space S= {GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO}
Random variable X is Selected, which represents number of times orange O' is spun, which is given by
X=0,1,2,3
Probability of an event = [tex]\frac{\text{Total favorable outcome}}{\text{Total Possible outcome}}[/tex]
X=0, Probability of Orange(O), in G G G = [tex]\frac{1}{8}[/tex]
X=1, Probability of Orange(O), in G G O , GOG,and O G G, 3 in total = [tex]\frac{1}{8}[/tex]
X=2, Probability of Orange(O), in G O O , O GO,and O O G, 3 in total = [tex]\frac{1}{8}[/tex]
X=3, Probability of Orange(O), in O O O, 1 in all= [tex]\frac{1}{8}[/tex]
