A probability experiment was conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12}, event F= {6,7,}, and event G={9,10,11,12}. Assume that each outcome is equally likely. List the outcomes of F and G?. find P(F or G) by counting the number of outcomes. Determine P(F or G) using the general addition rule.

To list the outcomes of events F and G, you simply need to identify the elements that belong to each event:

Event F: {6, 7}
Event G: {9, 10, 11, 12}

Now, to find P(F or G) by counting the number of outcomes, you need to determine the total number of outcomes in events F or G.

The number of outcomes in event F is 2 (since there are two elements: 6 and 7).
The number of outcomes in event G is 4 (since there are four elements: 9, 10, 11, and 12).

To find the total number of outcomes in F or G, you need to add the number of outcomes in F and G, but you also need to account for any shared outcomes.

In this case, there are no shared outcomes, so the total number of outcomes in F or G is 2 + 4 = 6.

Next, to determine P(F or G) using the general addition rule, you can use the formula:

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

Since each outcome is equally likely, the probability for any individual outcome is 1 divided by the total number of outcomes. In this case, the total number of outcomes is 12.

P(F) = 2/12 = 1/6
P(G) = 4/12 = 1/3
Since there are no shared outcomes between F and G, P(F and G) = 0.

Therefore, applying the general addition rule:

P(F or G) = P(F) + P(G) - P(F and G)
P(F or G) = 1/6 + 1/3 - 0
P(F or G) = 1/6 + 2/6
P(F or G) = 3/6
P(F or G) = 1/2