determine p(f or g) using the general addition rule

Question

determine p(f or g) using the general addition rule

s=1,2,3,4,5,6,7,8,9,10,11,12

event f=4,5,6,8

event g=9,10,11,12

Answer 1

n(s) = the number of elements in set s = 12

n(f) = the number of elements in set f = 4

n(g) = the number of elements in set g = 4

 

The probabilites are:

 

     p(f) = n(f)/n(s) = 4/12 = 1/3

     p(g) = n(g)/n(s) = 4/12 = 1/3

 

The addition rule is:

 

     p(f or g) = p(f) + p(g) = 1/3 + 1/3 = 2/3

 

Note that you can also compute p(f or g) as follows:

 

     f or g = 4,5,6,8,9,10,11,12

 

     so n(f or g) = 8

 

     p(f or g) = n(f or g)/n(s) = 8/12 = 2/3