Learning Goal: I’m working on a statistics question and need an explanation and answer to help me learn.
Use this activity to explore how probability is used in statistical inference.
You are studying with one of your classmates who is acing this class. She displays the following picture.
Then she pulls out a new deck of cards. She removes the plastic wrap from the deck of new cards, opens the box, and pulls out the cards. She removes the jokers and any other cards not displayed in the picture above. Then she starts shuffling the cards – which is difficult because the cards are brand new and slippery. She continues to shuffle and reshuffle until you agree that the deck is well-shuffled. Then she sets the deck down.
To verify that you know how to calculate various probabilities for a randomly drawn card, she asks the following questions which you answer correctly.
Then your classmate says, “O.K. Let’s make a little bet. If you draw a black card, I will help you with all remaining homework in this class.” If not, you must wash and wax my car for me. Since she opened a brand new deck of cards right in front of you and you verified they were well-shuffled, you know the probability of drawing a black card is 0.5 or 50%, so you agree to the bet.
She picks up the deck of cards, fans them out (face down of course), and asks you to randomly select a card. You select a card and turn it over. It’s red – not black.
You set the card aside and ask to try again. She reluctantly agrees and warns that if you lose, you will have to wash and wax her car twice. But if you win, you will not have to wash and wax her car, and she will help you with your homework as promised. You draw another card. It’s red – not black.
You set the card on top of the previously drawn red card and ask to try a third time. Again, she reluctantly agrees, and you draw another card. It’s red – not black. You must now wash and wax her car three times. You decide to quickly calculate the probability of randomly selecting a sample of three red cards.
2652⋅2551⋅2450≈0.1176 or 11.76%
You set the card on top of the previously drawn red cards and think, “The next card has to be black.” You ask to try a fourth time. Again, she reluctantly agrees, and you draw another card. It’s red – not black. You now have a random sample of 4 red cards, and you must wash and wax her car four times.
You set the card on the stack of previously drawn red cards, and ask to try again. Once again, she reluctantly agrees, and you draw another card.
Use the Module 14 discussion board (opens in a new tab) to ask questions or provide feedback about the problems in any Module 14 activity – including this peer-reviewed assignment.
Click the “Next” or > button to continue.
Content by Cuyamaca College math faculty and inspired by Dr. Roxy Peck.
Peer Review (FD Optional)
|This criterion is linked to a Learning OutcomeFirst Attempt||
|This criterion is linked to a Learning OutcomeAnswering the Prompt||
|This criterion is linked to a Learning OutcomePeer Review||
|Total Points: 10|
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