Law of Large Numbers

Front

What is the Law of Large Numbers about?

Back

Probability

Front

If you toss a fair coin 10,000 times and it lands on heads 4989 times, does the experimental probability and theoretical probability become further away from each other?

Back

False

Front

How many guesses would you like to be allowed in a 'Guess the Number of Jelly Beans in the Jar' contest to maximize your chances of winning?

Back

1,000

Front

What does the Law of Large Numbers state?

Back

As a probabilistic process is repeated a large number of times, the experimental probability of its possible outcomes will get closer to their respective probabilities.

Front

If you toss a coin 100 times and it lands on heads every time, what is the probability it will land on tails the 101st toss?

Back

1/2

Front

Define experimental probability.

Back

Experimental probability is the ratio of the number of times an event occurs to the total number of trials conducted.

Front

Define theoretical probability.

Back

Theoretical probability is the likelihood of an event occurring based on all possible outcomes, calculated as the number of favorable outcomes divided by the total number of outcomes.

Front

What is an example of a situation where the Law of Large Numbers applies?

Back

Tossing a fair die multiple times; as the number of tosses increases, the experimental probability of rolling each number approaches 1/6.

Front

What is the difference between experimental and theoretical probability?

Back

Experimental probability is based on actual experiments, while theoretical probability is based on expected outcomes.

Front

What happens to the experimental probability as the number of trials increases?

Back

It gets closer to the theoretical probability.