Determine P(F or G) using the General Addition Rule.

Question

In problems 5-12, 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}. Let event F = {5, 6, 7, 8, 9} and event G = {9, 10, 11, 12}. Assume that each outcome is equally likely.

 

*7. List the outcomes in F or G. Now 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.

**The answer should be P(F or G) = 2/3 ...just not sure how to get to the answer.

Answer 1

Note that F and G share the outcome 9.

 

P(F or G) = P(F) + P(G) - P(F and G)

              = 5/12 + 4/12 - 1/12

              = 8/12

              = 2/3