Stacked deck of cards, certainty, & compound events & probability
Questioning is the foundation of all learning.
The first step in rejecting not knowing is to ask, why?
Sweetland
Introductory script
Prepare a stacked deck of black only cards.
Start with:
- I am going to give the first person who draws a red card a snack pack.
- Who wants to try.
- Have a learner draw a card, observe, return the card to the deck shuffle, and ask for another person who wants to draw.
- Continue, until they begin to believe there is no red card in the deck.
Ask. How many draws do you think it wouild take to be certain there are not red cards in the deck?
Discuss.
Pose this suggestion:
Let's use a regular deck of cards and explore how many times by chance it would be possible to draw four or five cards of one color in a row.
Ask.
- What is the likelihood of the first card being black? 26:52, 1/2, .050, 50%
- What is the likelihood of the second card being black?
- Does the first card being black affect the second card being black? Assuming the card is returned to the deck.
- What is the likelihood of the second card being black?
During the dicussion, at an appropriate time, share the red black tree and black tree.
We are going to explore compound events of probability. (for independent events.) Independent events
May want to introduce experimental and theoretical probabilty models.
When learners understand how the compound probabilities are determined, return to the original question.
After how many draws would you be certain that no red cards are in the deck?
While you may be sure, it is not impossible.
One way to state your certainty is with a percentage. Like the weather forcast.
Mathematicians, scientist, statisticians, use .05 as a point to be sketical that a pure chance event is likely.
Expansion activity
Prepare a bag with 10 colored tiles (7 yellow and red).
When drawing three tiles what is the probaility of two being yellow? Of all three being yellow?
If this is done experimentally,
Use a bag with 10 colored tiles, 7 yellow and red,. Draw a tile, record, replaceit, draw a second, record, draw a third, and record. If groups do this enough times so the total of the class is 100, then,
we find it doesn't work like the cards (probability of drawing three red or black was the same). Here the probabilities of drawing three yellow and three red are not the same.
Since the probabilities are not the same, we need a different strategy.
How about a tree with probabilities?
How does the theoretical using this tree compare with the experimental?
Interesting!
Resources
Probability tree for red and black card draw from a deck of cards
Black only card deck probability tree
Tiles - three black seven yellow tree
