PROBABILITY HIGH-LOW CARD TASK

The student will calculate probabilities. Key concepts include:

a) Conditional probability

b) Dependent and independent events

c) Addition and multiplication rules

d) Counting techniques (Permutations & Combinations)

e) Law of Large Numbers

Name: _____________________________________________ Date: __________________

Game Rules

The rules are easy. Pick a card and then determine whether or not the next card will be higher or lower.  The only catch is that you will have to be finding the probability of the next card being higher or lower to inform your decision. For the sake of these examples, calculate the probability out of 52 for each card in the deck.

You will be given two different scenarios.

I. Scenario 1:

Pick a card and guess whether the next card will be higher or lower. Before you pick the card, however, you will find the probability of that card being higher or lower. After you pick the card, you will shuffle the cards back into the deck and repeat the process for a total of 15 times.

II. Scenario 2:

In the second scenario, you will do the same process. Pick a card; find the probability of the card being higher or lower. Instead of taking the cards and shuffling them back into the deck, you will decide whether the next card will be higher or lower than the card you just drew. Repeat this process for a total of 15 times as well, calculating the probability of each event occurring.

Questions

1.  Think of Independent and Dependent events. Which scenario is represented by an independent event and which one is dependent? Explain your reasoning.

1. Did the Theoretical probability of an event occurring match up with your experiment? If not, why do you think this is so?

1. What effect did the Independent vs. Dependent events have on the probability of an event occurring?

1. Let’s say we used multiple decks of cards to each scenario. Would the probabilities change? Explain your reasoning.

1. Predict what would happen if we changed the game rules. Instead of looking for a high or a low card, you will be looking for a number card or a face card (ace included). How would the probability change for an independent event? How about for a dependent event?

Data Collection: Scenario 1

Data Collection: Scenario 2

RESULTS/CONCLUSION

Write a summary statement to describe your findings and explain your results.

What do you still wonder about from doing this task?