The Monte Carlo fallacy would most likely lead you to:

• A. Assume that each coin toss is not independent of previous tosses
• B. Believe that after a long sequence of $\mathrm{heads}$ in coin tosses, a $\mathrm{tail}$ is 'due' to occur soon
• C. Expect that the probability of heads increases after several tails in a row
• D. Correctly calculate the probability of getting $3$ heads in a row as $\frac{1}{8}$

Answer: (B)

Verified step by step guidance

1. Understand the concept of the Monte Carlo fallacy, which is the mistaken belief that past independent events affect the probabilities of future independent events.
2. Recognize that in coin tosses, each toss is independent, meaning the outcome of previous tosses does not influence the next toss.
3. Identify that the fallacy leads people to think that after a long sequence of heads, a tail is 'due' to occur soon, even though the probability remains constant at 0.5 for each toss.
4. Recall that the probability of getting 3 heads in a row is calculated by multiplying the probability of heads on each toss: \(\left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{8}\).
5. Conclude that the Monte Carlo fallacy is about incorrectly assuming dependence between independent events, leading to wrong expectations about future outcomes.