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.

The Wink Game 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.

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

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.

Two-Child Family In 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.

Combined Results Wink/Blink/Stare. Two-Child Family (before activity) Combined Results Wink/Blink/Stare Two-Child Family (before activity) (after activity)

Dice Survey 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.

We’re making progress, right? … 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? …

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.”

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.”