Master Probability Fundamentals: A Comprehensive Guide for Pharmacy Students

Question 1

How many events can be defined on a sample space with 7 elements?

Accepted Answer

128

Answer

5

Answer

14

Answer

256

Question 2

Which event is an example of a compound event?

Accepted Answer

Tossing two coins and getting heads on both

Answer

Selecting a red ball from a bag of balls

Answer

Rolling a die and getting an even number

Answer

Drawing a card from a deck and getting a spade

Question 3

Which rule for calculating the probability of an event is incorrect?

Accepted Answer

The probability of the sample space is 0.

Answer

The probability of an event cannot be greater than 1.

Answer

The probability of an event cannot be less than 0.

Answer

The sum of the probabilities of all possible events is always 1.

Question 4

A bag contains 4 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a blue ball?

Accepted Answer

1/3

Answer

1/2

Answer

2/3

Answer

3/5

Question 5

Which is an example of a conditional probability?

Accepted Answer

The probability of rolling a 6 on a die, given that the previous roll was an even number

Answer

The probability of rolling a 6 on a die

Answer

The probability of selecting a heart from a shuffled deck

Answer

The probability of getting heads when flipping a coin

Question 6

Which type of probability distribution is suitable to model the number of defects in a manufactured product?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Exponential distribution

Answer

Uniform distribution

Question 7

In a sample space with 5 possible outcomes, what is the probability of an event with 2 favorable outcomes?

Accepted Answer

0.4

Answer

0.2

Answer

0.6

Answer

0.8

Question 8

Which of the following is NOT an axiom of probability?

Accepted Answer

The probability of the intersection of two events is equal to the sum of their probabilities.

Answer

The probability of an event cannot be negative.

Answer

The probability of the sample space is 1.

Answer

The probability of the union of two events is equal to the sum of their probabilities.

Question 9

An experiment involves tossing a coin twice. What is the sample space for this experiment?

Accepted Answer

{HH, HT, TH, TT}

Answer

{H, T}

Answer

{H1, T1, H2, T2}

Answer

{Head, Tail}

Question 10

What is the conditional probability of event A occurring given that event B has already occurred?

Accepted Answer

P(A) / P(B)

Answer

P(A)

Answer

P(B)

Answer

P(B) / P(A)

Question 11

Which of the following statements about the probability of an event is true?

Accepted Answer

It is always between 0 and 1.

Answer

It can be negative.

Answer

It can be less than 0 or greater than 1.

Answer

It is expressed as a percentage.

Question 12

Two events, A and B, are independent if:

Accepted Answer

P(A ∩ B) = P(A) × P(B)

Answer

P(A ∩ B) = P(A) + P(B)

Answer

P(A|B) = P(A)

Answer

P(B|A) = P(B)

Question 13

Given a sample space of {1, 2, 3, 4, 5}, what is the probability of obtaining a multiple of 2?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/5

Question 14

If events A and B are independent, what is the probability of both A and B occurring?

Accepted Answer

P(A) * P(B)

Answer

P(A) - P(B)

Answer

P(A) + P(B)

Answer

P(B) / P(A)

Question 15

Which of the following is not a recognized type of probability distribution?

Accepted Answer

Mean distribution

Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Question 16

Given a random variable X with mean μ=5 and variance σ^2=4, what is the standard deviation of X?

Accepted Answer

2

Answer

1

Answer

4

Answer

8

Question 17

If a data set exhibits a positively skewed distribution, what does it indicate?

Accepted Answer

The data is spread out more towards higher values

Answer

The data is spread out more towards lower values

Answer

The data is normally distributed

Answer

The data is uniformly distributed

Question 18

Which of these is a non-parametric statistical test?

Accepted Answer

Chi-square test

Answer

t-test

Answer

ANOVA

Answer

Regression

Question 19

What is the primary purpose of a confidence interval?

Accepted Answer

To estimate the true population value

Answer

To confirm a hypothesis

Answer

To predict future values

Answer

To summarize the characteristics of a data set

Question 20

Which of the following statements about probability is **incorrect**?

Accepted Answer

Probability can be a negative value.

Answer

Probability is a value between 0 and 1.

Answer

Probability is used to make predictions.

Answer

Probability is a measure of uncertainty.

Question 21

A sample space represents the set of all possible  ______ that can occur in an experiment.

Accepted Answer

outcomes

Answer

events

Answer

hypotheses

Answer

variables

Question 22

What is the probability of rolling an even number on a standard six-sided die?

Accepted Answer

1/2

Answer

1/4

Answer

1/6

Answer

1/3

Question 23

The negation of an event 'A' is represented by:

Accepted Answer

A complement (A')

Answer

A itself

Answer

A union (A ∪)

Answer

A intersection (A ∩)

Question 24

A standard deck of 52 cards has 10 cards removed. What is the probability of drawing a red card from the remaining deck?

Accepted Answer

13/42

Answer

13/52

Answer

10/52

Answer

10/42

Question 25

Which of the following is **not** a component of Bayes' theorem?

Accepted Answer

Conditional independence

Answer

Prior probability

Answer

Likelihood

Answer

Posterior probability

Question 26

The probability density function of a normal distribution is given by:

Accepted Answer

(1/σ√(2π)) * e^(-(x-μ)²/(2σ²))

Answer

μ * e^(-(x-σ)²/(2π))

Answer

σ√(2π) * e^(-(x-μ)/(2σ²))

Answer

(1/σ²) * e^(-(x-μ)²) * (2π)

Question 27

Which of the following is a measure of the **spread** of a distribution?

Accepted Answer

Variance

Answer

Skewness

Answer

Mean

Answer

Probability