Probability is the measure of the likelihood that an event occurs. The problem requires you to determine what the probability is of 45 children being born on the same day of the week.

There are 7 days in a week. In a regular year there are 365 days which is equivalent to 52 whole weeks and one odd day. In a leap year there are 52 complete weeks and 2 odd days. The problem does not provide any information on whether the children are born in the same year, or if that is the case, which year they were born in. As a result, to determine the required probability we need to assume that each day of the year has an equal chance of being one of the seven days of the week, though this is not the case in reality.

Having assumed that each day has a probability of being a particular day of the week of 1/7, the probability of each of the 45 students having their birthdays on any particular day of the week is (1/7)^45. But as there are 7 days in a week, the probability that the children have their birthdays on the same day of the week is 7*(1/7)^45 = 1/7^44.

The required probability that 45 children have their birthdays on the same day of the week is ** approximately** 1/7^44.