Let's Play Cards! (A class activity for probability with playing cards) Note that this activity can be completed whether or not the previous activity with cards and sets was completed. This activity addresses the following learning objectives: 1) List and count by using systematic methods (product tables, tree diagrams). 2) Apply the Fundamental Counting Principle. 3) Apply the Factorial Formula. 4) Recognize the difference between a permutation and a combination. 5) Use permutations and combinations to solve counting problems. 6) Apply counting techniques to real world problems. 7) Recognize a probability experiment and list the sample space (possible outcomes) associated with such an experiment. 8) Determine the probability of a specific outcome in an experiment using simple, compound, and conditional probabilities. 1) You could also have online students complete this activity independently. If students don't have access to a deck of cards, you may instead use an image of a deck of cards such as eck.svg However, students won't have as much of a tactile experience. Instead, you could encourage students to copy the image repeatedly and then highlight/circle the relevant cards to encourage a bit more of a tactile experience. (Consider having students submit these images as part of their work.) Let's Play Cards! A single card is selected from a standard deck of cards. Let H be the event that a heart is selected. Let F be the event that a face card is selected. Find the following: SNCh hich U3 byt The size of the sample space: P(H) = P(F) = P(H and F) = P(HorF)= P(not H) = P(not F) = Now two cards are selected from the deck with replacement. 8. 9. 10. 11. 12. P(both cards are heads) with replacement = P(neither card is heads) with replacement = P(at least one card is heads) with replacement = P(both cards are face cards) with replacement = P(neither card is a face card) with replacement = Now two cards are selected from the deck without replacement. 13. 14, 15. 16. 17. 18. 19. 20. P(both cards are heads) without replacement = P(neither card is heads) without replacement = P(at least one card is heads) without replacement = P(both cards are face cards) without replacement = P(neither card is a face card) without replacement = How many ways are there to select a poker hand of five cards from a deck of cards? Find the probability of selecting a poker hand that consists of all black cards. Find the probability of selecting a poker hand that consists of all hearts