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Two events A and B are independent events if the occurrence of one event does not affect the occurrence of the other. It is also said that they are independent if and only if the probability that both events occur is equal to the product of the individual probabilities.
Let G, B, and O be the events of drawing green, blue, and orange marbles, respectively. The probability of first picking a green marble can be calculated by dividing the favorable outcomes by the possible outcomes. The bowl currently contains 3 marbles in total, 1 of which is green. P( G)= 1/3 Suppose that the first marble is replaced before the second draw. After the replacement of the first marble drawn, there are again 3 marbles in the bowl, 1 of which is orange. P( O)= 1/3 Note that there are 9 possible outcomes for drawing two marbles if the marbles are drawn one at a time and then replaced before the next drawing. Only 1 of these options corresponds to an event of drawing a green marble and then an orange marble. G G G B G O B B B G B O O O O G O B Therefore, the combined probability of picking a green marble first and an orange marble second is 19. Since the probability of both events occurring equals the product of the individual probabilities, the events are independent. 1/3* 1/3 = 1/9 [0.3em] ā [0.3em] P( G)* P( O)=P( Gā O)