Question

1. Write by hand, the formula for the counting rule of an experiment with k-steps with nk outcomes each. This is a process of randomly selecting k numbers (or objects) with replacement (or repetition). Look for the formula in your notes, PowerPoint slides or textbook.

Answer 1

Answer:

         $\large\boxed{\large\boxed{(n_k)^k}}$

Explanation:

The formula for the counting rule of an experiment with k-steps with $n_k$outcomes each. This is a process of randomly selecting k numbers (or objects) with replacement (or repetition). Look for the formula in your notes, PowerPoint slides or textbook.

• For the first step you have: $n_k$  posibble outcomes

• For the second step you have:  $n_k$  posibble outcomes

• For the third step you have:  $n_k$  posibble outcomes

• For the k-step you have:  $n_k$  posibble outcomes

Thus,  a per the Fundamental Counting Principle or counting rule, the number of possible outcomes is:

           $n_k\cdot n_k\cdot n_k\cdot ...\cdot n_k$

That is $n_k$ multiplied by itself k time, which is $n_k$ raised to power $k$.

      $(n_k)^k$