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?
The coin has no idea what the result of previous tosses was. The probability of heads on the next toss is 0.5 unless it is an asymmetrical coin.
The concept of the "law of averages" is a common misconception when it comes to probability. In reality, the previous outcomes of independent events (like coin tosses) do not affect the probabilities of future outcomes. Each coin toss is an independent event, and the probability of heads or tails remains the same regardless of previous outcomes.
To calculate the probability of heads or tails on the next toss, you need to consider that a fair coin has two equally likely outcomes: heads (H) and tails (T). Therefore, the probability of getting either heads or tails on any individual toss is 1/2, or 0.5.
So, no matter how many times the coin has landed on heads in a row (in this case, 5 times), the probability of heads on the next toss is still 0.5, and the probability of tails is also 0.5. The outcome of one toss does not influence the outcome of subsequent tosses.