Bart and Lisa are playing a coin-tossing game where each player tosses a fair coin 20 times consecutively. The winner of the game is the player who tosses the most consecutive tails. Bart decides to go first and tosses tails five times in a row. Marge and Homer are observing the game and make the following observations before Bart attempts the sixth toss: Marge: "The probability of Bart tossing tails has to be greater than 75% because he is on a roll!"
Homer: "No, Marge, the probability of Bart tossing tails has to be less than 25% because he hasn't tossed heads in the last five tosses and he is due to toss heads!"
A behavioral economist would conclude that Marge's statement is an example of the __________, and Homer's statement is an example of the ___________.

Question

Quizplus · Accepted Answer

Marge's statement is an example of the hot-hand fallacy, which assumes that a player's chance of winning increases if they have been winning previously. However, in reality, each coin toss is independent of the previous ones and the probability of getting a tails remains the same.
Homer's statement is an example of the gambler's fallacy, which assumes that random events are influenced by previous events. However, in reality, each coin toss is independent of the previous ones and the probability of getting a heads or tails remains the same.

Bart and Lisa Are Playing a Coin-Tossing Game Where Each