Final answer:
There is a 3.125% chance of flipping five tails in a row when flipping a coin. This percentage comes from raising the probability of a single tail (0.5) to the power of five. The law of large numbers implies that repeating this coin flip sequence extensively would yield results approximating this probability.
Step-by-step explanation:
The probability of obtaining five tails in a row when flipping a coin is found by multiplying the probability of getting tails on a single flip by itself five times, since each flip is an independent event with a probability of 0.5 for tails.
Thus, (0.5)^5 = 0.03125, which means there is a 3.125% chance of flipping five tails in a row.
When considering the event of a coin being flipped five times and repeating this experiment ten thousand times, we invoke the law of large numbers.
This law states that as the number of trials of an experiment increases, the experimental probability (or relative frequency) of a given outcome approaches the theoretical probability.
Therefore, if we were to actually flip a coin five times for ten thousand trials, the number of times five tails in a row occurred would likely be close to the theoretical probability of 3.