a student claims that if a fair coin is tossed and comes up heads 5 times in a row, then according to the law of averages the probability of tails on the next toss is greater than the probability of heads. What is your reply?

That each toss is independent and the probability of heads on the next toss is 0.5

Believe Damon.

The probability of getting six heads in a row is very small ([1/2]^6 = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2). However, once you have tossed 5 heads in a row, the probability of getting a head on the sixth toss is still 1/2 = .5.

I hope this helps a little more.

The concept of "the law of averages" is a common misconception. In reality, the law of averages doesn't exist. Each coin toss is an independent event, meaning it has no impact on previous or future tosses. Therefore, the probability of getting heads or tails on the next toss does not change based on the outcome of previous tosses.

In this case, if the coin is fair, the probability of getting heads or tails on any given toss is always 50%. The previous outcome of getting heads 5 times in a row does not affect the probability of getting heads or tails on the next toss. Each toss is a fresh event with the same 50% chance for either outcome.

To explain further, if you toss a fair coin 5 times and get heads on each toss, the probability of getting heads on the 6th toss is still 50%. The probability of getting tails on the next toss is also 50%. The outcome of each toss is completely independent of the previous tosses.

In conclusion, the student's claim is incorrect. The law of averages does not dictate that the probability of tails is greater than the probability of heads after a string of heads. Each coin toss is a stand-alone event, and the probability is always 50% for either outcome.

the probability is that yes it would land on heads.