MATH 110 MODULE 6: PROBABILITY
AND PROBABILITY DISTRIBUTIONS
2026/2027 UPDATE. JUST RELEASED
1. In probability theory, if two events A and B are mutually exclusive, what is the value of P(A
and B)?
A. 1.0
B. 0.0
C. 0.5
D. P(A) + P(B)
Answer: B
Conceptual Explanation: Mutually exclusive events cannot occur at the same time, so the
probability of their intersection is zero.
2. What is the primary characteristic of a Binomial Distribution?
A. The trials are dependent on each other.
B. The probability of success changes with each trial.
C. There are exactly two possible outcomes for each trial.
D. The number of trials is infinite.
,Answer: C
Conceptual Explanation: A binomial distribution represents the number of successes in a
fixed number of independent trials where each trial has only two outcomes: success or
failure.
3. Which of the following describes the ‘Law of Large Numbers’?
A. As the number of trials increases, the experimental probability approaches the
theoretical probability.
B. Small samples provide better estimates of the population mean.
C. Probability always remains constant regardless of sample size.
D. The sum of all probabilities in a sample space equals zero.
Answer: A
Conceptual Explanation: The Law of Large Numbers states that as the number of
experiments increases, the relative frequency of an event converges to its theoretical
probability.
4. In a Standard Normal Distribution, what are the mean (mu) and standard deviation
(sigma)?
A. mu = 1, sigma = 0
B. mu = 0, sigma = 1
C. mu = 100, sigma = 15
, D. mu = 0, sigma = 0
Answer: B
Conceptual Explanation: By definition, the standard normal distribution (Z-distribution)
is centered at 0 with a spread of 1.
5. If P(A) = 0.4 and P(B) = 0.5, and A and B are independent events, what is P(A and B)?
A. 0.2
B. 0.1
C. 0.9
D. 0.45
Answer: A
Conceptual Explanation: For independent events, P(A and B) = P(A) * P(B). Thus, 0.4 * 0.5
= 0.2.
6. What is the total area under the curve of any continuous probability density function?
A. Depends on the mean
B. 1.0
C. 0.5
D. Infinity
Answer: B
AND PROBABILITY DISTRIBUTIONS
2026/2027 UPDATE. JUST RELEASED
1. In probability theory, if two events A and B are mutually exclusive, what is the value of P(A
and B)?
A. 1.0
B. 0.0
C. 0.5
D. P(A) + P(B)
Answer: B
Conceptual Explanation: Mutually exclusive events cannot occur at the same time, so the
probability of their intersection is zero.
2. What is the primary characteristic of a Binomial Distribution?
A. The trials are dependent on each other.
B. The probability of success changes with each trial.
C. There are exactly two possible outcomes for each trial.
D. The number of trials is infinite.
,Answer: C
Conceptual Explanation: A binomial distribution represents the number of successes in a
fixed number of independent trials where each trial has only two outcomes: success or
failure.
3. Which of the following describes the ‘Law of Large Numbers’?
A. As the number of trials increases, the experimental probability approaches the
theoretical probability.
B. Small samples provide better estimates of the population mean.
C. Probability always remains constant regardless of sample size.
D. The sum of all probabilities in a sample space equals zero.
Answer: A
Conceptual Explanation: The Law of Large Numbers states that as the number of
experiments increases, the relative frequency of an event converges to its theoretical
probability.
4. In a Standard Normal Distribution, what are the mean (mu) and standard deviation
(sigma)?
A. mu = 1, sigma = 0
B. mu = 0, sigma = 1
C. mu = 100, sigma = 15
, D. mu = 0, sigma = 0
Answer: B
Conceptual Explanation: By definition, the standard normal distribution (Z-distribution)
is centered at 0 with a spread of 1.
5. If P(A) = 0.4 and P(B) = 0.5, and A and B are independent events, what is P(A and B)?
A. 0.2
B. 0.1
C. 0.9
D. 0.45
Answer: A
Conceptual Explanation: For independent events, P(A and B) = P(A) * P(B). Thus, 0.4 * 0.5
= 0.2.
6. What is the total area under the curve of any continuous probability density function?
A. Depends on the mean
B. 1.0
C. 0.5
D. Infinity
Answer: B
