The following are the two statements relating to the theory of probability. Indicate the statements…
Both statements are correct: by the multiplication theorem of probability, for two independent events A and B, P(A ∩ B) = P(A) × P(B) (Statement I); and for dependent…
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The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect. Statement (I) : The probability of the joint occurrence of independent events A and B is equal to the probability of A multiplied by the probability of B or vice versa. Statement (II) : The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditional probability of B when A has occurred or vice versa.
Answer and explanation
Correct answer A
Both statements are correct: by the multiplication theorem of probability, for two independent events A and B, P(A ∩ B) = P(A) × P(B) (Statement I); and for dependent events, the joint probability equals the marginal probability of one event multiplied by the conditional probability of the other given that the first has occurred: P(A ∩ B) = P(A) × P(B | A) (Statement II).
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