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Two events A and B are considered dependent events if the occurrence of either event affects the occurrence of the other. If the events are dependent, the probability that both events occur is equal to the product of the probability of the first event occurring and the probability of the second event occurring after the first event.
Let G, B, and O be the events of drawing green, blue, and orange marbles, respectively. The probability of first picking the 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 after the green marble is drawn, it is not replaced in the bowl.
This affects the probability of picking the orange marble on the second draw. Now there is still 1 orange marble in the bowl, but instead of 3, there are 2 marbles in total in the bowl. P( O| G)= 1/2 The sample space of the situation can be found using this information. G B G O B G B O O G O B Out of the 6 possible outcomes, only 1 outcome corresponds to first drawing the green marble and then the orange marble. Therefore, the probability of picking the green and then the orange marble is 16. 1/3* 1/2 = 1/6 [0.3em] ⇓ [0.3em] P( G) * P( O| G) = P( G ⋂ O) Because the occurrence of the first event affects the occurrence of the second, these events can be concluded to be dependent.