If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be A. disjoint. B. the sample space. C. independent. D. collectively exhaustive.

Let Ω be the sample space and A⊆Ω be an event. Given below are two statements:(S1): If P(A)=0, then A=ϕ(S2): If P(A)=1, then A=ΩThenonly (S1) is trueonly (S2) is trueboth (S1) and (S2) are trueboth (S1) and (S2) are false

Consider the experiment of flipping a coin. Which statement is true?a. Events can be mutually exclusive but not collectively exhaustiveb. Events can be collectively exhaustive but not mutually exclusivec. Cannot be determined from the information givend. Events can be mutually exclusive and collectively exhaustive

1. Two events are considered independent if: a) The occurrence of one event affects the occurrence of the other event. b) The occurrence of one event does not affect the occurrence of the other event. c) The occurrence of one event guarantees the occurrence of the other event. d) The occurrence of one event is impossible without the occurrence of the other event. 2. The formula for calculating the probability of independent events is: a) P(A ∩B) = P(A) * P(B) b) P(A ∩B) = P(A) + P(B) c) P(A ∩B) = P(A) / P(B) d) P(A ∩B) = P(A) - P(B) 3. If A and B are independent events, what is the probability of both events occurring? a) P(A ∩B) = P(A) * P(B) b) P(A ∩B) = P(A) + P(B) c) P(A ∩B) = P(A) / P(B) d) P(A ∩B) = P(A) - P(B) 4. Two events are considered dependent if: a) The occurrence of one event does not affect the occurrence of the other event. b) The occurrence of one event affects the occurrence of the other event. c) The occurrence of one event guarantees the occurrence of the other event. d) The occurrence of one event is impossible without the occurrence of the other event. 5. The formula for calculating the probability of dependent events is: a) P(A ∩B) = P(A) * P(B) b) P(A ∩B) = P(A) + P(B) c) P(A ∩B) = P(A) / P(B) d) P(A ∩B) = P(A) - P(B) 6. If A and B are dependent events, and A occurs first, what is the probability of both events occurring? a) P(A ∩B) = P(A) * P(B) b) P(A ∩B) = P(A) + P(B) c) P(A ∩B) = P(A) / P(B) d) P(A ∩B) = P(A) - P(B) 7. In the multiplication rule of probability for independent events, what is the relationship between P(A) and P(B)? a) P(A) = P(B) b) P(A) ≠ P(B) c) P(A) > P(B) d) P(A) < P(B) 8. In the multiplication rule of probability for dependent events, what is the relationship between P(A) and P(B|A)? a) P(A) = P(B|A) b) P(A) ≠ P(B|A) c) P(A) > P(B|A) d) P(A) < P(B|A) 9. If two events are independent, what is the probability of both events not occurring? a) P(A') * P(B') b) 1 - (P(A) * P(B)) c) P(A') + P(B') d) 1 - (P(A) + P(B)) 10. If two events are dependent, what is the probability of both events not occurring? a) P(A') * P(B') b) 1 - (P(A) * P(B)) c) P(A') + P(B') d) 1 - (P(A) + P(B))

wo events having nonzero probabilities can be both mutually exclusive and independent cannot be both mutually exclusive and independent are always mutually exclusive are always independent

A subset of sample space to which a probability is assigneda. Complementb. Experimentc. Eventd. None