Week7

Question 1

What are the main aims of studying probability in experimental research?

Answer 1

To understand probability’s role, learn its formal definition, grasp basic rules, explore conditional probability and independence, and introduce probability densities and distributions.

Question 2

Why is probability important in experimental research?

Answer 2

Probability helps measure randomness in relation to systematic, predictable outcomes in experiments.

Question 3

What is logical probability?

Answer 3

It’s probability defined by the structure of a question, such as the probability of a coin toss landing heads.

Question 4

What is empirical probability?

Answer 4

Probability based on observed or historical data, like the probability of rain or risk of disease.

Question 5

How do we interpret a probability of 0.5?

Answer 5

It means that, over many trials, the event is expected to occur about half the time.

Question 6

What is the frequentist interpretation of probability?

Answer 6

It sees probability as the expected frequency of an event over repeated trials.

Question 7

What are the basic rules of probability?

Answer 7

The total probability rule, complement rule, addition rule, and multiplication rule.

Question 8

What is the total probability rule?

Answer 8

The probability of all possible outcomes in an experiment sums to 1.

Question 9

What is the complement rule in probability?

Answer 9

If

p is the probability of an event, the probability of it not occurring is
1−p.

Question 10

What is the addition rule in probability?

Answer 10

For two events A and B, P(A or B)= P(A)+P(B) - P(A and B)

Question 11

What is conditional probability?

Answer 11

The probability of event A occurring given that event B has occurred.

Question 12

How is conditional probability calculated?

Answer 12

P(A|B) = P(A and B)/ P(B)

Question 13

What are independent events?

Answer 13

Events where the occurrence of one does not affect the probability of the other.

Question 14

How is joint probability calculated for independent events?

Answer 14

P(A and B) = P(A) x P(B)

Question 15

What is a probability distribution?

Answer 15

A model that shows the probabilities of different outcomes in an experiment.

Question 16

What are categorical variables in probability?

Answer 16

Variables that represent distinct categories, such as nominal or ordinal data (e.g., heads or tails).

Question 17

What is probability density?

Answer 17

The probability of a specific outcome occurring in an experiment.

Question 18

What is cumulative distribution?

Answer 18

The probability of all outcomes less than or equal to a particular value.

Question 19

Why is it harder to assign exact probabilities to continuous variables

Answer 19

Because there are infinitely many possible values; instead, probabilities are assigned to ranges.

Question 20

How do histograms and probability distributions differ?

Answer 20

Histograms show observed frequencies, while probability distributions model expected frequencies and aid in hypothesis testing.