Final answer:
The probability that none of the three people selected were born on the same day of the week is the product of individual probabilities for each selection: 7/7 for the first, 6/7 for the second, and 5/7 for the third person. This calculates to 30/49, which is not listed in the provided options.
Step-by-step explanation:
The question asks about the probability that none of the three people selected at random were born on the same day of the week. To solve this problem, we first consider that there are seven days in a week. The first person can be born on any day of the week (7 out of 7 chances). The chance that the second person is born on a different day than the first is 6 out of 7 (since one day is already taken). Similarly, the probability that the third person is born on a different day than the first two is 5 out of 7 (since two days are already taken).
To find the combined probability, we multiply these probabilities:
Probability = (7/7) × (6/7) × (5/7)
This simplifies to 30/49, which represents the probability that all three people have different birthdays in terms of the day of the week. None of the provided options match this probability, indicating there might have been an error in the question or the options provided.