Final answer:
The probability calculations depend on whether the sampling is with or without replacement, affecting the odds after each selection. For without replacement, the odds change with each draw, while with replacement they remain constant.
Step-by-step explanation:
When dealing with probabilities of selecting specific items from a set without replacement, it is important to account for the changing odds after each selection. For example, if two cellphones are randomly selected from a box of two yellow and seven green iPhones without replacement, the probability that both are green is calculated by multiplying the probability of selecting a green iPhone on the first draw by the probability of selecting another green iPhone on the second draw after the first one has been removed.
The steps to calculate this probability would be to take the number of green phones over the total number of phones for the first draw: 7/9 then multiply by the number of remaining green phones over the new total for the second draw: 6/8, resulting in a probability of (7/9)*(6/8). Similarly, for the scenario where the colors are mixed (one yellow and one green), the calculations would involve selecting a yellow and then a green or vice versa.
When sampling with replacement, the total number of phones remains constant, and the probability of selecting a certain color remains unchanged with each draw. This results in a different probability calculation than when sampling without replacement.