Question

for an in - class demonstration, a teacher flips a fair coin 5 times, and each of the 5 times it lands on heads. a student argues that it is more likely to land on tails on the next, or 6th, flip. is the student correct? explain your reasoning.

Explanation:

A fair coin has two independent outcomes (heads or tails) for each flip. The result of one flip does not affect the result of another flip. The probability of getting heads or tails on any single flip of a fair coin is always \(P(\text{heads})=\frac{1}{2}\) and \(P(\text{tails})=\frac{1}{2}\), regardless of previous results.

Answer:

The student is not correct. Each coin - flip is an independent event. The probability of getting tails on the 6th flip is still \(\frac{1}{2}\), just as it was for each of the previous 5 flips. The previous 5 heads do not influence the outcome of the 6th flip.