Miranda tosses a fair coin consecutively five times and gets heads each time.When her son Shane asks her about the probability of getting tails on the next (sixth)toss,Miranda says the following: "This is a fair coin,so I should toss heads approximately 50 percent of the time.Because I have tossed heads 100 percent of the time for my first five tosses,then the probability of me tossing tails on the sixth toss must be greater than 50 percent." Miranda's statement is an example of the ________ fallacy.
A) hot-hand
B) association
C) gambler's
D) dealer's
E) Showtime

Question

Quizplus · Accepted Answer

Miranda's statement is an example of the gambler's fallacy, which is the belief that if something happens frequently in the past, it is less likely to happen in the future. However, in reality, each coin toss is independent and has a 50 percent chance of resulting in either heads or tails, regardless of the previous results. Therefore, the probability of getting tails on the sixth toss is still 50 percent, even though Miranda has already gotten five heads in a row.

Miranda Tosses a Fair Coin Consecutively Five Times and Gets