Gambler's Fallacy can be illustrated by which statement about independent coin flips?

• A. Believing that past outcomes influence future outcomes in independent random events
• B. Each outcome is independent and equally probable
• C. A run of heads makes tails less likely overall
• D. The probability of heads increases after several tails

Answer: (A)

Believing that past outcomes influence future outcomes in independent random events. A fair coin flip has no memory: the chance of heads is 50 percent on every flip, no matter what happened before. The gambler's fallacy is the mistaken idea that a run of heads pushes the next flip toward tails, or that outcomes will balance out in the short run. Instead, the probability remains the same each time. That makes this statement the best illustration. The other descriptions either restate a fact about independence or misstate how outcomes behave, but they don’t capture the bias in reasoning that past results should influence the next one in an independent process.