Games

1. Read the printed scenario. Identify its cost, probability and total return.
2. Students calculate the expected net independently, then compare their reasoning in pairs.
3. Change only the total return. Find the return that makes the expected net zero.

Expected net is a probability-weighted average. Total return includes the original stake.

1. Read the ticket table. Calculate the average return on one ticket.
2. Use the purchase plan to calculate the total cost and expected net. Compare single tickets with full packs of ten.
3. Calculate the chance of no payout using the complement. Discuss why any payout does not guarantee a profit.

Expected value and the chance of finishing ahead are different quantities.

1. Use the rules printed on the question sheet. Predict which dice totals are most common.
2. List the 36 ordered pairs. Count the pairs that receive a payout and calculate the expected net.
3. Roll 20 times if dice are available. Compare that sample with the calculation; pool results across the class.

Equally likely pairs do not make every total equally likely.

1. Read the printed event probabilities and whether they are independent or conditional. Every event must succeed.
2. Draw a probability tree. Multiply along the all-success route, then calculate the expected net from the printed price.
3. For the default three independent 50% events, use three fair coins and count all-heads results. Discuss why a short sample need not match the calculation.

The chance of every event happening is smaller than each individual chance.

1. Read the situation and the two choices on the question sheet.
2. Calculate each choice’s game-win probability. Write a decision and one assumption it depends on.
3. Imagine the preferred choice loses. Discuss whether that outcome changes the earlier reasoning.

Decision quality and the result of one attempt are different.