In Exercises 1, 2, and 3 assume that the year has 366 days and all birthdays are equally likely. In Exercise 19 assume it is equally likely that a person is born in any given month of the year. 1. a)...

In Exercises 1, 2, and 3 assume that the year has 366 days and all birthdays are equally likely. In Exercise 19 assume it is equally likely that a person is born in any given month of the year.

1. a) What is the probability that two people chosen at random were born on the same day of the week?

b) What is the probability that in a group of
n
people chosen at random, there are at least two born on the same day of the week?

c) How many people chosen at random are needed to make the probability greater than 1/2 that there are at least two people born on the same day of the week?

2. Find the smallest number of people you need to choose at random so that the probability that at least one of them has a birthday today exceeds 1/2.

3. Find the smallest number of people you need to choose at random so that the probability that at least two of them were both born on April 1 exceeds 1/2.