A fair coin is tossed ten times and lands heads every time. What is the probability that the coin lands tails on the next toss?

Understanding the Problem

The question asks for the probability of a fair coin landing tails on the next toss, regardless of the outcomes of the previous tosses.

Relevant Concepts

1. Independence of Events: Each toss of a fair coin is independent of the previous tosses. This means that the outcome of one toss does not affect the outcome of another toss.
2. Probability of a Fair Coin: For a fair coin, the probability of landing on heads (H) or tails (T) is equal: $P(H) = P(T) = \frac{1}{2}$

Analysis and Detail

1. Since the outcome of the coin tosses is independent, the probability of the coin landing tails on the next toss remains $\frac{1}{2}$, despite the fact that the first ten tosses resulted in heads.

2. The independence of coin tosses indicates that past results do not influence future outcomes. Therefore, the ten heads do not change the fact that the next toss is still a fair toss.

Verify and Summarize

To summarize, the historical data (10 heads in this case) does not affect the fair nature of the coin. The probability of getting tails on the next toss remains:

$P(T) = \frac{1}{2}$

Final Answer

The probability that the coin lands tails on the next toss is $\frac{1}{2}$.