Gamblers often falsely predict the outcome of a future trial based on the outcome of previous trials. When trials are independent, we cannot predict the outcome of a future trial based on the outcomes of previous trials.

For each of the following examples, (i) state whether the trials are independent or dependent and (ii) explain why. In addition, (iii) state whether it is possible that the quote is accurate or whether it is definitely fallacious, explaining how the independence or dependence of trials influences this.

a. You are playing Monopoly and have rolled a pair of sixes in 4 out of 10 of your last rolls of the dice. You say, “Cool. I’m on a roll. I’m likely to get sixes again on my next turn.”

b. You are an Ohio State University football fan and are sad because they have lost two games in a row.

You say, “That is really unusual; the Buckeyes are doomed this season. That’s what happens with lots of early-season injuries.”

c. You have a 20-year-old car that often has trouble starting. It has started every day this week, and now it’s Friday. You say, “I’m doomed. It’s been reliable all week, and even though I did get a tune-up last week, today is bound to be the day it fails me.”

d. It’s your first week of your corporate internship and you have to wear nylon stockings to the office if you’re wearing a skirt. On the first and second days, you get a run in your stockings almost immediately, an indication of a defect. The third day, you put on yet another new pair of stockings and say, “OK, this pair has to be good. There’s no way I’d have three bad pairs in a row. They’re even from different stores!”