Probability Quizzes for Pharmacy Students: Test Your Knowledge

Question 1

Which theorem calculates the probability of an event occurring, given the occurrence of another event?

Accepted Answer

Bayes' theorem

Answer

Central Limit theorem

Answer

Poisson distribution theorem

Answer

Uniform distribution theorem

Question 2

For a discrete random variable X, what is the formula to calculate its expected value?

Accepted Answer

E(X) = Σ(x_i * p_i)

Answer

E(X) = Σ(p_i / x_i)

Answer

E(X) = Σ(x_i - p_i)

Answer

E(X) = Σ(p_i - x_i)

Question 3

Which characteristic does NOT describe a normal distribution?

Accepted Answer

Right-skewed

Answer

Symmetrical

Answer

Bell-shaped

Answer

Unimodal

Question 4

What is the probability density function for a uniform distribution defined over the interval [a, b]?

Accepted Answer

f(x) = 1 / (b - a)

Answer

f(x) = (b - a) / 2

Answer

f(x) = 1 / (2 * (b - a))

Answer

f(x) = (b - a) / 1

Question 5

Which value represents the standard deviation of a binomial distribution with parameters n and p?

Accepted Answer

sqrt(n * p * q)

Answer

sqrt(n * p)

Answer

sqrt(n * q)

Answer

sqrt(p + q)

Question 6

Which application best demonstrates the use of Bayes' theorem in pharmacy?

Accepted Answer

Calculating the probability of a patient responding to a specific treatment

Answer

Determining the likelihood of a drug interaction

Answer

Estimating the prevalence of a disease

Answer

Predicting the side effects of a medication

Question 7

Which fundamental axiom of probability states that the probability of any event A is always non-negative?

Accepted Answer

P(A) >= 0 for all events A

Answer

P(S) = 1, where S is the sample space

Answer

P(A union B) = P(A) + P(B) - P(A intersect B)

Answer

P(A complement) = 1 - P(A)

Question 8

Two events A and B are independent if:

Accepted Answer

All of the above conditions

Answer

P(A|B) = P(A)

Answer

P(B|A) = P(B)

Answer

P(A intersect B) = P(A) * P(B)

Question 9

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn without replacement, what is the probability that at least one of the marbles is red?

Accepted Answer

1/5

Answer

1/15

Answer

1/10

Answer

1/3

Question 10

Which probability distribution is known for its bell-shaped curve?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 11

The mean of a probability distribution represents its:

Accepted Answer

Expected value

Answer

Median

Answer

Mode

Answer

Standard deviation

Question 12

Which measure of dispersion represents the average squared deviation from the mean?

Accepted Answer

Variance

Answer

Range

Answer

Kurtosis

Answer

Mean

Question 13

A random variable X follows a uniform distribution on the interval [0, 1]. What is its probability density function?

Accepted Answer

f(x) = 1 for x in [0, 1]

Answer

f(x) = x for x in [0, 1]

Answer

f(x) = 1/x for x in [0, 1]

Answer

f(x) = 2x for x in [0, 1]

Question 14

Which of the following is a property of Bayes' Theorem?

Accepted Answer

It requires prior knowledge about the probabilities of events.

Answer

It is asymmetric.

Answer

It is transitive.

Answer

It is only applicable to independent events.

Question 15

A fair six-sided die is rolled twice. What is the probability of obtaining a 3 on the first roll and a 5 on the second roll?

Accepted Answer

1/36

Answer

1/6

Answer

1/12

Answer

1/24

Question 16

A pharmaceutical company claims that their new drug is 80% effective in treating a certain disease. If a patient is treated with this drug, what is the probability that the treatment will be successful?

Accepted Answer

0.8

Answer

0.86

Answer

0.72

Answer

0.64

Question 17

Let X be a random variable with mean μ and variance σ^2. If Y = 3X + 2, what is the mean of Y?

Accepted Answer

3μ + 2

Answer

4μ + 2

Answer

μ + 2

Answer

μ - 2

Question 18

On a fair six-sided die, find the probability of rolling a 6?

Accepted Answer

1/6

Answer

1/4

Answer

1/5

Answer

1/3

Question 19

What type of probability is used to determine the likelihood that a student will pass a test given that they have studied?

Accepted Answer

Conditional probability

Answer

Joint probability

Answer

Independent probability

Answer

Marginal probability

Question 20

What is Bayes' Theorem?

Accepted Answer

A theorem that calculates the probability of an event based on prior knowledge or evidence.

Answer

A theorem that calculates the probability of a union of events.

Question 21

What's the probability distribution of the sum of two independent random variables?

Accepted Answer

The convolution of the two probability distributions

Answer

The product of the two probability distributions

Answer

The sum of the two probability distributions

Question 22

What is the expected value of a random variable?

Accepted Answer

The weighted average of all possible outcomes

Answer

The most likely outcome

Answer

The median outcome

Answer

The standard deviation of the outcomes

Question 23

What is the variance of a random variable?

Accepted Answer

The average of the squared differences between each outcome and the expected value

Answer

The square of the standard deviation

Answer

The difference between the maximum and minimum outcomes