Final answer:
The probability of the marble being in one of the first three slices of the cake is 7/9, which is approximately 0.78.
Step-by-step explanation:
To calculate the probability that the marble will be in one of the first three slices of the cake, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. In this case, the favorable outcomes are the marbles that are green, and the total number of possible outcomes is the total number of marbles.
There are 4 green marbles out of a total of 9 marbles in the bag. Therefore, the probability of drawing a green marble is 4/9. Since the question asks for the probability of the marble being in one of the first three slices, we also need to consider the red marbles. There are 3 red marbles, so the total number of favorable outcomes is 4 green marbles + 3 red marbles = 7 marbles.
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Therefore, the probability of the marble being in one of the first three slices of the cake is 7/9, which is approximately 0.78.