Master Probability Fundamentals: A Comprehensive Guide for Nursing Students

Question 1

An event is best described as:

Accepted Answer

A subset of the sample space

Answer

A specific outcome of an experiment

Answer

A measure of the likelihood of an outcome

Answer

A mathematical model of a random experiment

Question 2

According to one of the probability axioms, the probability of an impossible event is always:

Accepted Answer

0

Answer

1

Answer

0.5

Answer

Indeterminate

Question 3

Which of the following properties states that the probability of an event must fall within the range of 0 and 1?

Accepted Answer

Non-negativity

Answer

Normalization

Answer

Additivity

Answer

Complementation

Question 4

Mutually exclusive events are characterized by which of the following properties?

Accepted Answer

P(A and B) = 0

Answer

P(A or B) = P(A) + P(B)

Answer

P(A and B) = P(A) * P(B)

Answer

P(A or B) = P(A) * P(B)

Question 5

The correct formula for calculating the posterior probability, P(A | B), is:

Accepted Answer

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

Answer

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

Answer

P(A | B) = P(A) + P(B | A)

Answer

P(A | B) = P(B) - P(A | B)

Question 6

Which of the following is NOT an axiom of probability?

Accepted Answer

The probability of the intersection of two events is equal to the number of favorable outcomes divided by the total number of possible outcomes.

Answer

The probability of an event cannot be negative or greater than 1.

Answer

The probability of the sample space is equal to 1.

Answer

The probability of the union of two mutually exclusive events is the sum of their probabilities.

Question 7

A standard six-sided die is rolled. What is the probability of rolling an even number?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Question 8

Which of the following collections of sets is a sigma-algebra?

Accepted Answer

The set of all subsets of a sample space

Answer

The set of all events with probability greater than 0

Answer

The set of all mutually exclusive events

Answer

The set of all independent events

Question 9

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 10

Which of the following is the most appropriate graphical representation for a quantitative variable?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Scatter plot

Answer

Line plot

Question 11

A researcher wants to estimate the population mean of a normally distributed population. Which of the following sampling methods is most likely to produce the most accurate estimate?

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Systematic sampling

Question 12

What is the term for the set of all possible outcomes in a probability experiment?

Accepted Answer

Sample space

Answer

Event

Answer

Probability distribution

Answer

Outcome set

Question 13

An event with a probability of zero is known as a:

Accepted Answer

Impossible event

Answer

Likely event

Answer

Certain event

Answer

Independent event

Question 14

Which property of conditional probability states that P(A|B) cannot exceed P(A)?

Accepted Answer

P(A|B) ≤ P(A)

Answer

P(A|B) = P(B|A)

Answer

P(A|B) can be greater than 1

Answer

P(A|B) is always equal to 0.5

Question 15

Which characteristic of a fair coin toss ensures that the outcomes of successive tosses are independent?

Accepted Answer

The previous outcome does not influence the next outcome

Answer

The coin is perfectly symmetrical

Answer

The coin has equal probability of landing on heads or tails

Answer

The coin is flipped in the air

Question 16

Which statement about probability axioms is INCORRECT?

Accepted Answer

The probability of an event may have a negative value.

Answer

The probability of a sample space is always 1.

Answer

The sum of probabilities of mutually exclusive events equals their combined probability.

Answer

The probability of an event lies between 0 and 1.

Question 17

What is the complement of 'obtaining a heads' when flipping a coin?

Accepted Answer

Obtaining a tails.

Answer

Rolling an even number on a die.

Answer

Rolling a number greater than 3 on a die.

Answer

Drawing an ace from a deck of cards.

Question 18

Which scenario represents a conditional probability?

Accepted Answer

Likelihood of developing a fever, given the presence of a cold.

Answer

Probability of obtaining heads on a coin flip.

Answer

Probability of rolling a 6 on a die.

Question 19

Which of the following is an example of a dependent event?

Accepted Answer

Drawing the second card from a deck after the first card has been drawn.

Answer

Flipping a coin twice.

Answer

Rolling a die and then flipping a coin.

Question 20

Which represents a permutation?

Accepted Answer

Arranging 5 letters in a specific order.

Answer

Selecting and replacing a card from a deck.

Answer

Rolling and obtaining a specific number on a die.

Answer

Choosing 2 people from a group of 10 without regard to order.

Question 21

What distinguishes a permutation from a combination?

Accepted Answer

In permutations, order matters; in combinations, it does not.

Answer

Permutations involve selecting items, while combinations involve arranging items.

Answer

The value of permutations is always greater than that of combinations.