Which of the following best describes the Law of Large Numbers?As a coin is flipped a greater number of times, we would expect more heads than tails on average.We are more likely to roll a 3 or a 4 the more times we roll a dice.The average value of all of our dice rolls will converge upon 3.5 the more times we roll the dice.The more times we flip a coin, the more likely we are to predict which side it will land on.
Question
Which of the following best describes the Law of Large Numbers?As a coin is flipped a greater number of times, we would expect more heads than tails on average.We are more likely to roll a 3 or a 4 the more times we roll a dice.The average value of all of our dice rolls will converge upon 3.5 the more times we roll the dice.The more times we flip a coin, the more likely we are to predict which side it will land on.
Solution
The statement that best describes the Law of Large Numbers is: "The average value of all of our dice rolls will converge upon 3.5 the more times we roll the dice."
The Law of Large Numbers is a principle of probability that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
In the context of rolling a dice, the expected value is 3.5 (since it's the average of all possible outcomes: 1, 2, 3, 4, 5, and 6). So, the more times we roll the dice, the closer our average result will get to 3.5.
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