Question

In a simulation of coin​ tosses, a streak of 15 heads has appeared. The Law of Large Numbers says which of the following must be​ true?

A. The 16th flip is more likely to come up tails.
B. The simulation was designed incorrectly.
C. The empirical probability will not match the theoretical probability if more trials are completed due to the streak.
D. It is equally likely that the 16th toss will be a head or a tail.

Answer 1

The Law of Large Numbers states that the overall long-term observed relative frequency of heads in a coin toss simulation will approach the theoretical probability of 0.5. Therefore, it is equally likely that the 16th toss will be a head or a tail, regardless of the previous streak of heads.

Step-by-step explanation:

The Law of Large Numbers states that as the number of repetitions of an experiment is increased, the relative frequency obtained in the experiment tends to become closer and closer to the theoretical probability. This means that if you continue to flip a coin, the overall long-term observed relative frequency of heads will approach the theoretical probability of 0.5.

Therefore, for the given scenario of a streak of 15 heads in a simulation of coin tosses, the Law of Large Numbers suggests that it is equally likely that the 16th toss will be a head or a tail. The previous streak of heads does not influence the outcome of the next toss, as each toss of the coin is independent and has a 50% chance of resulting in a head or a tail.

So, the correct answer is D. It is equally likely that the 16th toss will be a head or a tail.