Math 221 - Chapter 5

Variables or events that are not associated are called​ what? Categorical Dependent Random Independent

Independent note: When two events are​ independent, the probability of one event occurring is not affected by whether or not the other event occurs.

When events A and B are said to be​ independent, what does that​ mean? Choose the correct answer below. A. Knowledge that event B occurred does not change the probability of event A occurring. B. Events A and B are complements. C. Events A and B are equally likely to occur. D. Knowledge that event B occurred changes the probability of event A occurring.

A. Knowledge that event B occurred does not change the probability of event A occurring. note: If knowledge that event B occurred does not change the probability of event A​ occurring, then events A and B are independent.

Which of the following cannot be used to represent a discrete probability​ distribution? Tables Equations Areas under curves Graphs

Areas under curves can only represent continuous probability distributions. They cannot represent discrete probability distributions.

What does a probability distribution​ indicate? A. The probability of each outcome of a random experiment B. All the possible outcomes of a random experiment C. Both A and B D. None of the above

C. Both A and B A probability distribution indicates the possible outcomes of a random experiment and the probability that each of those outcomes will occur.

Which of the following might be a reason that an empirical probability found through a simulation does not match the theoretical​ probability? A. The empirical value is just varying. Doing more trials will get closer to the theoretical probability. B. The theoretical value is incorrect. C. Both A and B are correct. D. Neither A nor B are correct.

C. Both A and B are correct. note: People are not​ infallible; the theroetical value may be incorrect due to a miscalculation. In​ addition, empirical values vary. Doing more trials will get closer to the theoretical probability.

Probabilities where the focus is on just one group of objects and a random sample is taken from that group alone are called​ what? Categorical probabilities Mutually exclusive probabilities Conditional probabilities Random probabilities

Conditional probabilities note; When examining a population of people where some are single and some are​ married, the probability of a married person having a college degree is one example of a conditional probability.

What are numerical variables with outcomes that cannot be listed or counted because they occur over a range​ called? Normal Probable Continuous Discrete

Continuous

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.

D. It is equally likely that the 16th toss will be a head or a tail. note: The Law of Large Numbers is patient. It says that the empirical probability will equal the true probability after infinitely many trials. A streak of 10 or 20 or even 100​ heads, though extremely​ rare, does not contradict the LLN.

In​ statistics, for what does the abbreviation​ "pdf" stand? Probability discrete function Probability distribution frequency Probability delivery function Probability distribution function

Probability distribution function

If an experiment with a random outcome is repeated a large number of​ times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called​ what? The Law of Binomial Probability The Law of Simulation The Law of Large Numbers The Random Number Table

The Law of Large Numbers note: The Law of Large Numbers states that if an experiment with a random outcome is repeated a large number of​ time, the empirical probability of an event is likely to be close to the true probability. The larger the number of​ repetitions, the closer together these probabilities are likely to be.

Determine the best number to fill in the blank. In most​ cases, it is recommended that at least how many trials be done when using a simulation to estimate a​ probability? 1000 100 10 None of these

answer: 100

The total area under a probability density curve​ _____.

equals 1

If events A and B are​ independent, what must be done to find the probability of event A AND​ B? A. Multiply the probability of A and the probability of B. B. Divide the probability of A and the probability of B. C. Subtract the probability of A and the probability of B. D. Add the probabilities of A and the probability of B.

note: This formula is often called the multiplication rule.

Often, conditional probabilities are worded with what​ phrase? ​"dependent" ​"given that" ​"either/or" ​"mutually exclusive"

​"given that" note: One example is being asked to find​ "the probability that a randomly selected person is married given that the person has a college​ degree."