1.
What does the law of large numbers mean?
Correct Answer
B. No matter how many times you try, the probability remains the same.
Explanation
The law of large numbers states that as the number of trials or experiments increases, the average outcome will approach the expected value or probability. In other words, regardless of how many times you try, the probability of a certain event occurring will remain constant. This principle is fundamental in probability theory and statistics, providing a basis for understanding random events and their long-term behavior.
2.
The Law of Large Numbers deals with what?
Correct Answer
B. Probability.
Explanation
The Law of Large Numbers states that as the number of trials or experiments increases, the observed results will more closely approach the expected or theoretical probability. In other words, it deals with the concept of probability and how it becomes more reliable and accurate with a larger sample size. It has nothing to do with running for a long time, geometry shapes, or algebraic equations.
3.
What is the term for someone who doesn't understand the Law of Large Numbers?
Correct Answer
D. Gambler's fallacy.
Explanation
The term for someone who doesn't understand the Law of Large Numbers is "Gambler's fallacy". The Law of Large Numbers states that the more times an event is repeated, the closer the observed results will be to the expected probability. The Gambler's fallacy is a misconception where individuals believe that previous outcomes in a random event will affect future outcomes. This misunderstanding leads to irrational beliefs and behaviors, particularly in gambling, where individuals may falsely believe that if an event hasn't occurred for a while, it is more likely to happen soon.
4.
If you flip a coin 40 times and get heads every time. What is the likelihood of flipping a tails the 41st time?
Correct Answer
C. 1/2
Explanation
The likelihood of flipping a tails on the 41st flip is 1/2. This is because the outcome of each coin flip is independent of the previous flips. Regardless of the previous 40 flips resulting in heads, the probability of getting heads or tails on the 41st flip is always 1/2.
5.
If you roll to dice, what is the likelihood that you will roll two numbers that are the same?
Correct Answer
D. 1/36
Explanation
The likelihood of rolling two numbers that are the same can be calculated by finding the probability of rolling the same number on the first dice (1/6) and then multiplying it by the probability of rolling the same number on the second dice (1/6). This gives us a probability of 1/36.
6.
If you have a color wheel and there are four colors, what is the likelihood you will spin the color you want?
Correct Answer
D. 1/4
Explanation
The likelihood of spinning the color you want is 1 out of 4, or 1/4. This is because there are four colors on the color wheel, and you have only one specific color that you want. Therefore, the probability of spinning that specific color is 1 out of the total of 4 colors available.
7.
If you are spinning a color wheel with seven colors on it and you have 100 spins to get a red. After 99 spins you have gotten every color but red. What is the chance you will spin a red on the 100th spin?
Correct Answer
D. 1/7
Explanation
The chance of spinning a red on the 100th spin is 1/7. This is because each spin is independent of the others, so the probability of spinning a red on any given spin is always 1/7, regardless of the previous spins.
8.
True or False: The more you roll a die,the more likely you are to get a higher number.
Correct Answer
B. False.
Explanation
Rolling a die is a random process where each roll is independent of the previous ones. The probability of getting a higher number does not increase with more rolls. Each roll has an equal chance of landing on any number on the die, regardless of the number of previous rolls. Therefore, the statement that the more you roll a die, the more likely you are to get a higher number is false.
9.
True or False: If you roll a die 12 times and never get a one, the 13th role will be a six.
Correct Answer
B. False.
Explanation
The statement is false because each roll of a die is an independent event and the outcome of one roll does not affect the outcome of the next roll. Therefore, the fact that a one has not been rolled in the previous 12 rolls does not guarantee that the 13th roll will be a six. The probability of rolling a six on the 13th roll is the same as any other roll, which is 1/6.
10.
If you are stranded on a desert and you can't get off until you role a six on a die, how many rolls will you ask for?
Correct Answer
D. Infinite.
Explanation
If you are stranded on a desert and can't leave until you roll a six on a die, the probability of rolling a six on any given roll is 1/6. However, the probability of not rolling a six on any given roll is 5/6. Since each roll is independent of the previous rolls, the probability of not rolling a six on any roll is multiplied by the previous probability of not rolling a six. Therefore, the probability of never rolling a six is (5/6) * (5/6) * (5/6) * ... which is a never-ending sequence. Hence, you will need an infinite number of rolls to guarantee rolling a six.
11.
In your own words, explain the Law of Large Numbers.