Two experiments are to be performed the first can result in any one of m possible outcomes. if the first experiment results in outcome i, then the second experiment can result in any of n possible outcomes ,i=1,. what is the number of possible outcomes of the two experiments?

"i" varies according to the results of the first experiment. If i = 1, then experiment two has ni = (4)(1) outcomes. If i = 2, then the second experiment has ni = nm = (4)(2) = 8 outcomes as you have shown. 12 is the correct answer. You have offered a solution. Can you verify that this answer is correct? Make a new problem: This time experiment one has 3 possible outcomes (1,2,3). Let's still keep n = 4 for simplicity. Therefore, experiment two will have (4,8,12) outcomes that are dependent upon the result of experiment one.