determine P(F or G) by using the general addition rule

Question

a probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,1112} event F={4,5,6,8} and Event G={10,11,12}. assume the outcome of each 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.

Answer 1

By counting outcomes: P(F or G) = n(F or G)/n(S)

• n(S) = 12
• n(F) = 4
• n(G) = 3
• n(F and G) = 0  (Sets F and G do not intersect)
• n(F or G) = n(F) + n(G) - n(F and G) = 4 + 3 - 0 = 7
• P(F or G) = n(F or G)/n(S) = 7/12

 

Using the general addition rule: P(F or G) = P(F) + P(G) - P(F and G)

• P(F) = n(F)/n(S) = 4/12
• P(G) = n(G)/n(S) = 3/12
• P(F and G) = n(F and G)/n(S) = 0/12 = 0
• P(F or G) = 4/12 + 3/12 - 0 = 7/12