Question 1

According to set theory, a set is a well-defined collection of things and objects but not events.

Accepted Answer

In set theory, a set can be a collection of any distinct objects, including events, as long as they are well-defined and distinct.

Question 2

A subset of a larger set is also considered to be the universal set.

Accepted Answer

A subset is a portion of a larger set, therefore it cannot be considered the universal set. The universal set includes all possible elements that could be included in a set.

Question 3

The gambler's fallacy involves treating events that are independent of each other as dependent.

Accepted Answer

The gambler's fallacy is a mistaken belief that if something happens more frequently than normal during a certain period, it will happen less frequently in the future. It involves treating independent events as if they are dependent, which is a false assumption. For example, if a coin is flipped five times and lands on heads each time, the gambler's fallacy would suggest that it is more likely to land on tails on the next flip, which is not true since each flip is independent and has a 50/50 chance of landing on either heads or tails, regardless of previous outcomes.

Question 4

On tossing a coin, the probability of obtaining an outcome of HHHHHH is smaller than the probability of obtaining an outcome of HTHHHT.

Accepted Answer

Both outcomes have the same probability because each toss of a coin is an independent event with a probability of 1/2 for heads and 1/2 for tails, regardless of the sequence.

Question 5

The gambler's fallacy usually results in a correct judgement of probability of an outcome, even though the calculation of probability is not exactly correct.

Accepted Answer

The gambler's fallacy is a misconception that the probability of a random event is affected by previous events and is commonly seen in gambling situations. This fallacy can lead to incorrect judgment of probability as it disregards the fact that each event is independent and the probability remains the same for each occurrence.

Question 6

The probability of a given event that depends on the occurrence or non-occurrence of another event is known as conditional probability.

Accepted Answer

This is the correct definition of conditional probability.

Question 7

Consider 3 sets of events. As long as all three sets do not overlap, we can consider them mutually exclusive.

Accepted Answer

Mutually exclusive events mean that the occurrence of one event precludes the occurrence of the other(s) within the same experiment or trial. Simply not overlapping does not ensure they are mutually exclusive; they must also not be able to occur simultaneously.

Question 8

True or False: When there are five events in which the occurrence of one (event A) alters the probability of the occurrence of all the rest (events B, C, D, E), then events B, C, D and E are known as dependent on event A.

Accepted Answer

This is the definition of dependent events in probability. If the occurrence of one event affects the probability of the others, they are dependent on that event.

Question 9

Another term for events that are mutually exclusive is disjoint.

Accepted Answer

Mutually exclusive events are also known as disjoint events, meaning they have no outcomes in common.

Question 10

When two events are mutually exclusive, it means that when one occurs, the other event cannot occur.

Accepted Answer

This is the definition of mutually exclusive events. They cannot both occur at the same time.

Question 11

The gambler's fallacy is also known as the Monte Carlo fallacy.

Accepted Answer

The gambler's fallacy and Monte Carlo fallacy are two different names for the same concept - the false belief that past outcomes affect future outcomes in random events like gambling.

Question 12

An empirical set is a set of theoretical predictions.

Accepted Answer

An empirical set is a set of actual observations or measurements, not theoretical predictions.

Question 13

The probability of obtaining two sixes after rolling two dice is the same regardless of whether you roll the dice sequentially or simultaneously.

Accepted Answer

The probability of rolling a six on each die is 1/6. The probability of rolling two sixes sequentially is (1/6) * (1/6) = 1/36. The probability of rolling two sixes simultaneously is (1/6) * (1/6) = 1/36. Therefore, the probability is the same regardless of whether you roll the dice sequentially or simultaneously, making the statement true.

Question 14

When calculating the probability of obtaining a tail after a toss of a coin, the denominator of the formula is the number of events in a universal set.

Accepted Answer

The denominator of the probability formula is the total number of possible outcomes or events in the sample space, which is the universal set in probability theory.

Question 15

To calculate the probability of two independent events occurring, we add the probabilities of the occurrence of each event.

Accepted Answer

To calculate the probability of two independent events occurring together, we multiply the probabilities of each event occurring separately.

Question 16

The law of large numbers is a fallacy that results in an overestimation of the frequency of extreme outcomes.

Accepted Answer

The law of large numbers is a statistical concept that states that as the number of trials or samples increases, the actual results will get closer to the expected results. It is not a fallacy, but rather a proven principle. However, it is important to note that it does not guarantee that extreme outcomes will not occur, but rather that they become less and less likely as the number of trials increases.

Question 17

The probability of obtaining a 2, 4, or 5 on a roll of a die is the same as the probability of obtaining an odd number.

Accepted Answer

The probability of obtaining a 2, 4, or 5 is 3 out of 6 (or 1/2) since there are three favorable outcomes out of six possible outcomes on a die. The probability of obtaining an odd number (1, 3, or 5) is also 3 out of 6 (or 1/2), making both probabilities equal.

Question 18

In the law of large numbers, the "large numbers" refers to anything larger than 100.

Accepted Answer

The "large numbers" in the law of large numbers refer to an infinitely large sample size, not just anything larger than 100.

Question 19

The probability of obtaining a particular data point is the frequency of it occurring in the population.

Accepted Answer

The answer of The probability of obtaining a particular data...

Question 20

Inferential statistics allow you to evaluate whether a hypothesis is true or false.

Accepted Answer

Inferential statistics involve using sample data to make inferences about larger populations. This includes testing hypotheses and making decisions about whether they are true or false based on the data. Therefore, answer A is correct.

Quiz 7: Basic Probability Theory