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 equally likely outcomes (heads or tails) for each flip, and each flip is an independent event. This means the result of one flip does not affect the result of the next flip. The probability of getting heads ($P(H)$) and tails ($P(T)$) on any single flip of a fair coin is always $P(H) = P(T) = \frac{1}{2}$, regardless of previous results. So, the fact that the coin landed on heads 5 times before does not change the probability for the 6th flip; the likelihood of tails on the 6th flip is still $\frac{1}{2}$, same as heads. Thus, the student is incorrect.

Answer:

The student is not correct. Each coin flip is an independent event, and for a fair coin, the probability of landing on heads or tails on any single flip is always $\frac{1}{2}$, regardless of previous results. So, the likelihood of tails on the 6th flip is not more than the likelihood of heads.