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The Wink Game

In the cup are 2 chips. One chip has a dot ( ) on it and the other chip has a dash ( ). One chip is drawn from the cup. The symbol on the chip is recorded. The chip is placed back in the cup. A chip is drawn from the cup again. The symbol on the second chip is recorded.

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The Wink Game

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  1. In the cup are 2 chips. One chip has a dot ( ) on it and the other chip has a dash (). • One chip is drawn from the cup. • The symbol on the chip is recorded. • The chip is placed back in the cup. • A chip is drawn from the cup again. • The symbol on the second chip is recorded. • The chip is placed back in the cup. The Wink Game

  2. If this game is played many times which is more likely to happen? • Wink, Blink and Stare occur about the same      number of times. • Wink occurs more often. • Blink occurs more often. • Stare occurs more often. The Wink Game

  3. Responses from students in Introduction to Statistics (Math 1150) and Data Analysis & Probability for Middle School Teachers (Math 2450) at BGSU:

  4. Equiprobability Misconception Students demonstrating the equiprobability misconception assume that events related to a random experiment have an equal probability of occurring.  For example, if a coin is tossed 2 times, then the result will be 0 heads, 1 head or 2 heads.  Since there are 3 possible results for the number of heads, then each result has a probability of 1/3.

  5. Two-Child FamilyIn many families with two children, the number of boys and girls in the family is recorded. Which is more likely to happen? Having 2 girls, having 2 boys, and having 1 of each gender will occur about the same number of times. Having 1 of each gender will occur more often. Having 2 girls will occur more often. Having 2 boys will occur more often.

  6. Combined ResultsWink/Blink/Stare Two-Child Family (before activity) (after activity)

  7. Two fair six-sided dice are rolled many times. Let A be the event of rolling two even numbers, let B be the event of rolling two odd numbers, and let C be the event of rolling one even number and one odd number. Which is more likely to happen? • Events A, B, and C occur about the same number of times. • Event A occurs more often. • Event B occurs more often. • Event C occurs more often. Dice Survey

  8. Data Analysis & Probability for Middle School Teachers(Pre-service MCE with Math Concentration) Number of correct responses: Wink/Blink/Stare question: 4 2-Child Family question: 8 Dice survey: 10 We’re making progress, right? …

  9. Of the 10 students choosing the correct response on the dice survey, only 3 provided explanations showing correct reasoning, such as: “The options for two rolls are (E,E), (O,O), (E,O), or (O,E). Since there is 1 chance of events A and B and 2 chances of event C then C has a higher probability.”

  10. Examples of correct answer, but incorrect reasoning: • “In order for A or B to occur, the die has to land on even/odd twice in a row. With event C, that pressure is not there.” • “I would think that if one falls even, then more often than not, the next roll will be odd.” • “There is an equal chance of getting an odd and an even number.”

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