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the probability of event a occurs is 0.4 and the probability of event b occurs is 0.6. the probability of a occurs given b occurs is 0.45. a and b are independent events.

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Final answer:

The probability of two independent events A and B both occurring can be calculated by multiplying their individual probabilities, and the opportunity is 0.24.

Step-by-step explanation:

The question involves the concepts of independent events and conditional probability. Two events A and B are said to be independent if the probability of A occurring is not affected by the occurrence of B, and vice versa. In this case, events A and B are given to be independent.

The probability of event A occurring is 0.4 and the probability of event B occurring is 0.6. Since A and B are independent events, the probability of A and B both occurring is equal to the product of their individual probabilities: P(A AND B) = P(A) * P(B) = 0.4 * 0.6 = 0.24.

Therefore, the probability of A and B both occurring is 0.24.

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