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 event F and G, simply identify the elements that belong to each event.
Event F: {6, 7}
Event G: {9, 10, 11, 12}
Now, to find the probability of event F or G, we count the total number of outcomes and divide it by the total number of possible outcomes.
The total number of outcomes in the sample space (S) is 12, as given in the question.
Event F has 2 outcomes (6 and 7), and event G has 4 outcomes (9, 10, 11, 12).
To find the probability of event F or G, we need to count the number of outcomes that belong to either event F or G or both.
List of outcomes in F or G: {6, 7, 9, 10, 11, 12}
As you can see, there are 6 outcomes in total.
Using the general addition rule, we calculate P(F or G) by adding the probabilities of events F and G and subtracting the probability of their intersection (F ∩ G).
Since each outcome is equally likely, the probability of each outcome is 1/12.
Therefore, we have:
P(F or G) = P(F) + P(G) - P(F ∩ G)
= 2/12 + 4/12 - 0/12 (since F ∩ G = { }, there are no common outcomes in F and G)
= 6/12
= 1/2
So, the probability of event F or G is 1/2 or 0.5.