Probability Worksheet

This probability worksheet gives students eight real-world probability problems instead of abstract textbook setups. Every problem is grounded in something students can picture: drawing cards from a pile, rolling dice, timing a traffic light, or picking investments out of a portfolio. That framing is deliberate. Probability shows up constantly in financial decision-making, from assessing the odds an investment underperforms to weighing the risk built into a diversified portfolio.

The eight questions build in complexity. The first four are classic probability setups — a mixed pile of colored cards, a standard deck, a timed traffic light, and two dice rolled together — that let students practice basic probability rules, like favorable outcomes over total outcomes and simple compound events, before the stakes get more specific. The last four problems move into investment scenarios: picking stocks and bonds from a list, screening for bad investments in a portfolio, sorting employees at an investment bank by role, and evaluating a portfolio where investments fall into four different profitability tiers.

Several of the later questions require combinations rather than single-event probability, so this worksheet works best for students who already have some footing with combinations and compound probability, or as guided practice where you work the harder problems as a class before releasing students to finish independently. It pairs naturally with any unit connecting math to risk and investing, since every scenario after question four is framed around real financial decision-making rather than a generic word problem.

Below is the worksheet exactly as it appears in the Rapunzl curriculum, followed by teacher notes on how to use it in class.

This activity is from Module 22 of the Rapunzl curriculum, Financial Probabilities.

Probabilities In Real Life

This activity engages students in solving real-world probability problems and is crucial for understanding risk assessment and decision-making in financial contexts. We explore how to apply probability theory to everyday financial scenarios and hone analytical skills in risk evaluation, applying mathematical reasoning to financial decision-making processes.

Please work independently or in a small group to answer the following questions:

1. If a card is selected at random from a pile containing two red cards, four yellow cards, and 3 orange cards, what is the probability that it will be a yellow card?
2. If 1 playing card is picked at random from a deck of cards (52 cards), what is the probability that it is a
   • a. a heart?
   • b. a red card?
   • c. a King?
3. What is the probability of arriving at a traffic signal when it is green if the light is red for 25 seconds, yellow for 10 seconds, and green for 30 seconds?
4. Two dice are rolled and have their numbers added together. What is the probability that
   • a. the total is odd?
   • b. The total is 7?
   • c. That the total is less than six?
   • d. Any pair is rolled?
5. Three investments are selected at random from a list containing two stock picks and six different bonds. Find the probability that
   • a. both stocks are picked.
   • b. all of the picks are bonds.
   • c. one stock and two bonds are picked.
6. Five Investments are chosen at random from a list of 30 of which 5 are bad investments. What is the probability that at least one of the investments chosen are bad investments?
7. At an investment bank there are 28 employees. 13 work on the buy side, 10 work on the sell side, and the other 5 do administration work. Of the 13 working on the buy side, only 5 talk to clients.
   • a. What is the probability that an employee selected at random works on the buy side?
   • b. What is the probability that an employee selected at random will work on the buy side and with clients?
8. Three investments are chosen at random from a portfolio, the portfolio has 30 investments in it. Half are highly profitable, 5 are slightly profitable, 6 are break even, and 4 are losing money.

What is the probability that all three investments are profitable? What is the probability none of the investments are profitable?

Teacher Notes

Questions 1 through 4 are worth working as a warm-up before students see the investment-framed problems that follow. They isolate single-event and simple compound probability — a card pull, a card from a full deck, a timed light, two dice — without the added complexity of choosing multiple items from a group.

Starting at question 5, most problems ask students to find the probability of a specific combination of outcomes chosen from a set, not just a single draw. If your class hasn't covered combinations yet, this is the point to pause and reteach before assigning the rest of the worksheet, since questions 5, 6, and 8 all depend on that skill.

Question 7 is really two separate probability questions stacked in one scenario: the probability of working on the buy side, and then the probability of working on the buy side and talking to clients. Point out that the second part narrows the group used in part one, since students often try to recompute from all 28 employees again instead of building on their answer to part a.

Question 8 uses the word "profitable" loosely across two different groupings, since highly profitable and slightly profitable investments both count as profitable. It's worth clarifying that split with students before they start, rather than after they've already answered it a different way.

This worksheet is one piece of the full Financial Probabilities unit inside the Rapunzl teacher portal, where activities like this one sit alongside articles, guided practice, and a classroom investing simulator built for grades 6–12.

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