Q:

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 ni possible outcomes, i = 1, 2, . . . , m. What is the number of possible outcomes of the two experiments

Accepted Solution

A:
Answer: The first experiment has M probabilities, and the second has I(m) outcomes, that depends on the result of the first.And lets call m to the result of the first experiment.If the outcome of the first experiment is 1, then the second experiment has 1 possible outcome.If the outcome of the first experiment is 2, then the second experiment has 2 possibles outcomes.If the outcome of the first experiment is M, then the second experiment has M possibles outcomes.And so on.So the total number of combinations C is the sum of all the cases, where we exami1 outcome for m = 1 + 2 outcomes for m=2+...+M outcomes for m = MC = 1 + 2 + 3 + 4 +...Β΄+M