Question 1

If two events are mutually exclusive, then their joint probability is always zero.

Accepted Answer

Mutually exclusive events cannot occur at the same time, so the probability of both happening together is zero.

Question 2

A joint probability is the probability that at least one of two events occurs.

Accepted Answer

A joint probability is the probability of two events occurring simultaneously, not just at least one of them.

Question 3

The law of multiplication gives the probability that at least one of the two events will occur.

Accepted Answer

The law of multiplication gives the probability that two events will occur together (jointly), not that at least one will occur.

Question 4

If two events are mutually exclusive, then the two events are also independent.

Accepted Answer

Mutually exclusive events cannot occur at the same time, whereas independent events have no effect on the probability of each other occurring. If two events are mutually exclusive, the occurrence of one event means the other cannot occur, which directly influences the probability of the other event (making it 0), thus they cannot be independent.

Question 5

Given two events, A and B, if the probability of either A or B occurring is 0.6, then the probability of neither A nor B occurring is -0.6.

Accepted Answer

The probability of neither A nor B occurring is calculated as 1 minus the probability of either A or B occurring, which would be 1 - 0.6 = 0.4, not -0.6. Negative probabilities do not exist in probability theory.

Question 6

If the occurrence of one event does not affect the occurrence of another event, then the two events are mutually exclusive.

Accepted Answer

Two events are mutually exclusive if they cannot occur at the same time. The statement describes independent events, not mutually exclusive ones.

Question 7

An experiment is a process that produces outcomes.

Accepted Answer

An experiment is a process or study that results in the collection of data or outcomes.

Question 8

The method of assigning probabilities to uncertain outcomes based on laws and rules is called the relative frequency method.

Accepted Answer

The method described is known as the classical method. The relative frequency method assigns probabilities based on the frequency of events occurring over a large number of trials.

Question 9

The list of all elementary events for an experiment is called the sample space.

Accepted Answer

The sample space of an experiment is indeed the set of all possible outcomes, which are referred to as elementary events.

Question 10

In the conditional probability of P(E₁|E₂)is when E₂ has occurred and then the probability of E₁ occurring is determined.

Accepted Answer

Conditional probability P(E₁|E₂) is the probability of event E₁ occurring given that event E₂ has already occurred.

Question 11

Given two events, A and B, if the probability of A is 0.7, the probability of B is 0.3, and the joint probability of A and B is 0.21, then the two events are independent.

Accepted Answer

Two events, A and B, are independent if the probability of A and B occurring together (joint probability) is equal to the product of their individual probabilities. Here, 0.7 * 0.3 = 0.21, which matches the given joint probability, indicating independence.

Question 12

An event that cannot be broken down into other events is called a certainty outcome.

Accepted Answer

An event that cannot be broken down into other events is called an elementary event, not a certainty outcome. A certainty outcome is an event that is sure to happen.

Question 13

Assigning probabilities by dividing the number of ways that an event can occur by the total number of possible outcomes in an experiment is called the classical method.

Accepted Answer

The classical method of assigning probabilities is based on the assumption that all outcomes in the sample space are equally likely, and it calculates probabilities by dividing the number of favorable outcomes by the total number of possible outcomes.

Question 14

Probability is used to develop knowledge of the fundamental mathematical tools for quantitatively assessing risk.

Accepted Answer

Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is fundamental in assessing and quantifying risk in various fields such as finance, insurance, and engineering.

Question 15

Assigning probabilities to uncertain events based on one's beliefs or intuitions is called classical method.

Accepted Answer

Assigning probabilities to uncertain events based on one's beliefs or intuitions is called the subjective method. The classical method involves assigning probabilities based on equally likely outcomes.

Question 16

Inferring the value of a population parameter from the statistic on a random sample drawn from the population is an inferential process under uncertainty.

Accepted Answer

Inferential statistics involves making inferences about population parameters based on sample statistics, acknowledging that there is uncertainty due to sampling variability.

Question 17

If the probability that someone likes the color blue is 44% and the probability that among those individuals, the probability that they wake up early is 52%, then the probability that individuals who like the color blue and wake up early is about 23%.

Accepted Answer

The probability that individuals like the color blue and wake up early is found by multiplying the two probabilities: 0.44 * 0.52 = 0.2288, which is approximately 23%.

Question 18

The probability that a person's favorite color is blue would be an example of a marginal probability.

Accepted Answer

Marginal probability refers to the probability of a single event occurring without consideration of any other events, and in this case, it's the probability of someone's favorite color being blue, independent of any other factors.

Question 19

The probability of A $\cup$ B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.

Accepted Answer

The notation used (F1F1F1S1uf0c8F1F1F10) is unclear and does not directly relate to standard probability notation or the context provided about state and federal grants. Therefore, it's not possible to accurately determine the probability of the event described without further clarification or correct notation.

Question 20

If the occurrence of one event precludes the occurrence of another event, then the two events are mutually exclusive.

Accepted Answer

Mutually exclusive events are those that cannot happen at the same time, meaning if one event occurs, it prevents the occurrence of the other event.

Quiz 4: Probability