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= {3,6,7,}, and event G={9,10,12}. 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.

Do you use "outcome" to mean elementary events?

The elementary events of F are 3,6,7.

To list the outcomes of event F, we simply look at the elements in the set F={3,6,7}. Thus, the outcomes of event F are 3, 6, and 7.

Similarly, to list the outcomes of event G, we look at the elements in the set G={9,10,12}. Hence, the outcomes of event G are 9, 10, and 12.

Now, to find P(F or G) by counting the number of outcomes, we need to find the total number of outcomes in the union of events F and G, divided by the total number of outcomes in the sample space S.

The outcomes of event F or G are {3,6,7,9,10,12}, which contains 6 elements. The sample space S contains 12 elements. Therefore, P(F or G) by counting the number of outcomes is 6/12, which simplifies to 1/2 or 0.5.

To determine P(F or G) using the general addition rule, we need to calculate the probability of event F, the probability of event G, and subtract the probability of the intersection of events F and G, P(F and G).

The probability of event F is the number of outcomes in F divided by the total number of outcomes in the sample space S. Since F={3,6,7}, there are 3 outcomes in F, and the total number of outcomes in S is 12. Hence, P(F) = 3/12 = 1/4 or 0.25.

Similarly, the probability of event G is the number of outcomes in G divided by the total number of outcomes in S. As G={9,10,12}, there are 3 outcomes in G, and the total number of outcomes in S is 12. Therefore, P(G) = 3/12 = 1/4 or 0.25.

To calculate the probability of the intersection of events F and G, we find the number of outcomes that are common to both F and G, and then divide by the total number of outcomes in S. In this case, the common outcome is 0 (since F={3,6,7} and G={9,10,12} have no elements in common). Therefore, P(F and G) = 0.

Finally, using the general addition rule, we can calculate P(F or G) as follows:

P(F or G) = P(F) + P(G) - P(F and G)
= (1/4) + (1/4) - 0
= 1/2 or 0.5, which matches the result obtained by counting the number of outcomes.