To answer this question, we can use the concept of the birthday paradox. The birthday paradox states that in a group of people, the probability that at least two people have the same birthday is higher than what we might intuitively expect.
In this case, we are given that there are 26 children in Mrs. Melanie's class and that none of them were born on February 29th. We need to find the probability that at least two children have their birthdays on the same day.
To calculate this probability, we can use the complement rule. The complement of the event "at least two children have the same birthday" is the event "all children have different birthdays".
The probability that the first child has a unique birthday is 365/365 (since there are 365 possible days). The probability that the second child has a different birthday than the first is 364/365. Similarly, the probability that the third child has a different birthday than the first two is 363/365, and so on.
Therefore, the probability that all 26 children have different birthdays is:
(365/365) * (364/365) * (363/365) * ... * (340/365)
To find the probability that at least two children have the same birthday, we can subtract this probability from 1:
P(at least two children have the same birthday) = 1 - P(all children have different birthdays)
Now we can calculate the probability:
P(at least two children have the same birthday) = 1 - (365/365) * (364/365) * (363/365) * ... * (340/365)
Calculating this expression gives us approximately 0.60 or 60%.
Therefore, the correct answer is A) 60%.