Author(s):

Melissa Jackson (Utah State Univ.) and Kady Schneiter (Utah State Univ.)

**Instructions:**

- To begin at a different level, enter a number from one to eight in the box and click on 'Go.'
- Select a fish by clicking on or near it.
- Press the 'Done' button to indicate that you have made your selections.
- To answer a probability question, express the probability as a fraction and enter the numerator and denominator in the approrpriate boxes. Then click on 'Submit Answer'.
- If you are unsure of the probability, use the 'Hint' or 'See Solution' buttons to get help.
- From the solution screen, use the buttons to return to the previous level, repeat the current level, or move on to the next level.

**The Solution Screen:** For each level, the solution screen provides a brief explanation of the probability of the indicated event and a table illustrating how this probability could be found by listing all outcomes.

**The Solution Table:**

- Each cell in the table corresponds to one way in which the fish could have been selected.
- All possible outcomes are represented in the table.
- The order in which fish are arranged in a cell indicates the order of selection.

If the fish types were chosen randomly, all outcome would have the same probability. Thus the probability that an event occurs can be found by counting the number of outcomes that correspond to that event (these are highlighted in blue) and dividing by the total number of outcomes.

**Questions to consider:**

- Which fish did you select on Level 1? Be specific.
- Why is the probability of randomly selecting that fish 1/5?
- What is the probability of randomly selecting the type of fish you chose on Level 2?
- What would this probability be if you had chosen a different type of fish?
- On Level 3, how would the probability change if the types of fish were drawn with replacement instead of without replacement?
- On Level 3 and Level 4, did you use the addition rule or the multiplication rule to compute the probability? Explain in your own words why this rule must be used.
- On Level 5, after using the multiplication rule to calculate the probability of randomly selecting the two types of fish you chose in the order you chose them, why must you then double the probability?
- On Level 6, did you use the addition rule to compute the probability of randomly selecting the two fish you chose? Why or why not?
- How do Level 7 and Level 8 differ? How does this affect the probabilities you computed?

Melissa Jackson (Utah State Univ.) and Kady Schneiter (Utah State Univ.), "Probability Aquarium - Instructions and Questions for Student Investigation," *Convergence* (February 2010), DOI:10.4169/loci003313