Suppose we perform 2 experiments and this first experiment can result in any one of...

Alissa Hancock

Alissa Hancock

Answered

2022-07-07

Suppose we perform 2 experiments and this first experiment can result in any one of m possible outcomes. Suppose the first experiment results in outcome i. Then, the second experiment can result in any of n i possible outcomes i = 1 , . . , m. Q s : what is the number of possible outcomes of the two experiments?

Attempt:
If we have 1 , . . . , m possible outcomes and say this experiment results in one of them say i. and so second experiment can result in n i for each i so by multiplication principle we have n 1 n 2 . . n m possible outcomes. Is this correct?

Answer & Explanation

Jasper Parsons

Jasper Parsons

Expert

2022-07-08Added 7 answers

To have the outcomes implied by n 1 in the second experiment, we need outcome 1 in the first experiment ( E 1 = 1). Similarly we need outcome E 1 = 2 to get to those n 2 possibilities, etc.
So the possible second-experiment outcomes each depend on a given first-experiment result and the total outcome options are 1 m ( 1 n i ) = 1 m n i

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