STA301 Final Term Notes Set 2

LECTURE NO. 19

Relative Frequency Definition of Probability Axiomatic Definition of Probability Laws of Probability

Rule of Complementation Addition Theorem

MCQs:

Q1. What is the fundamental concept behind the relative frequency definition of probability?

1. Empirical evidence
2. Mathematical axioms
3. Subjective belief
4. Logical certainty

Answer: a) Empirical evidence

Q2. In the relative frequency definition, probability is defined as the limit of the relative frequency as ___________.

1. n approaches zero
2. n approaches infinity
3. m approaches zero
4. m approaches infinity

Answer: b) n approaches infinity

Q3. The relative frequency definition of probability is useful when ___________.

1. all outcomes are equally likely
2. classical definition is applicable
3. experiments are not repeated
4. outcomes are based on observations

Answer: d) outcomes are based on observations

Q4. In the coin-tossing example, Kerrich tossed a coin 10,000 times and obtained 5067 heads and 4933 tails. What was the proportion of heads?

1. 0.38
2. 0.47
3. 0.50
4. 0.514

Answer: d) 0.514

Q5. What is the term for the probability that is based on past evidence or underlying conditions, leading to non-quantifiable probabilities?

1. Statistical probability
2. Empirical probability
3. Axiomatic probability
4. Inductive probability

Answer: d) Inductive probability

Q6. The axiomatic definition of probability is based on a set of ___________.

1. Laws
2. Axioms
3. Observations
4. Experiments

Answer: b) axioms

Q7. According to Axiom 1 of probability, the probability of any event Ei must be

1. Equal to 1
2. Greater than 1
3. Between 0 and 1
4. Equal to 0

Answer: c) between 0 and 1

Q8. Axiom 2 states that the probability of the sample space S is ___________.

1. less than 1
2. equal to 1
3. greater than 1
4. equal to 0

Answer: b) equal to 1

Q9. According to Axiom 3, if events A and B are mutually exclusive, then P(A ∪ B) is equal to ___________.

1. P(A) - P(B)
2. P(A) × P(B)
3. P(A) / P(B)
4. P(A) + P(B)

Answer: d) P(A) + P(B)

Q10. What is the probability of the complement of an event equal to?

1. The probability of the event itself
2. One minus the probability of the event
3. The square root of the probability of the event
4. Twice the probability of the event

Answer: b) One minus the probability of the event