Please help me solve this

Question

A probability experiment is conducted in which the sample space of the experiment is Upper S={1, 2, 3,4,5,6,7,8,9,10,11,12} , event F={6,7,8} comma and event G={ 9,10,11,12} . 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.

Answer 1

The sample space S ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

We count how many outcomes are in S. We see that there are 12 outcomes.

For the event F={6, 7, 8} there are three desired outcomes.

For the event G={9, 10, 11, 12} there are 4 desired outcomes

The event F∪G has 7 outcomes:

F∪G={6, 7, 8, 9, 10, 11, 12}.

Therefore

P(F∪G)=7/12.