Final answer:
The probability that the four balls have the same color is calculated by considering the cases where all four balls are green and all four balls are white. The probability for each case is calculated by multiplying the probabilities at each step of selecting a ball of the same color. The final probabilities are approximately 1.178% for four green balls and 4.896% for four white balls.
Step-by-step explanation:
In order to find the probability that the four balls have the same color, you need to consider the two possibilities: either all four balls are green or all four balls are white. Let's calculate the probability for each case:
(A) Probability that all four balls are green:
The probability of selecting a green ball on the first draw is 7/16, since there are 7 green balls out of a total of 16.
Assuming a green ball is selected on the first draw, the probability of selecting another green ball on the second draw is 6/15, as there are now 6 green balls left out of 15.
Similarly, the probability of selecting a green ball on the third draw is 5/14, and on the fourth draw is 4/13.
Therefore, the overall probability of selecting four green balls in succession is (7/16) * (6/15) * (5/14) * (4/13).
(B) Probability that all four balls are white:
The calculation for selecting four white balls is similar to the calculation for selecting four green balls, but with different probabilities at each step.
The overall probability of selecting four white balls in succession is (9/16) * (8/15) * (7/14) * (6/13).
Therefore, the final answers are:
(A) The probability that the four balls have the same color is approximately 0.01178 or about 1.178%.
(B) The probability that the four balls have the same color is approximately 0.04896 or about 4.896%.