Final answer:
The probability that two people chosen at random were born on the same day of the week can be calculated using the principle of counting. 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 can be calculated using the complement rule. The number of people needed to make the probability greater than 1/2 that there are at least two people born on the same day of the week can be found by solving an equation.
Step-by-step explanation:
a) The probability that two people chosen at random were born on the same day of the week can be calculated using the principle of counting. There are 7 days in a week, so each person has a 1/7 chance of being born on any given day. Since there are two people, the probability that they were both born on the same day is (1/7) * (1/7) = 1/49.
b) To calculate 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, we can use the complement rule. The probability that no two people share the same birthday is 1 - (1/7) * (1/7) * ... * (1/7) (repeated n times). The complement of this probability is the probability that at least two people share the same birthday.
c) To find the number of people needed to make the probability greater than 1/2, we can set up an equation: 1 - (1/7) * (1/7) * ... * (1/7) (repeated n times) > 1/2. Solving this equation will give us the minimum value of n needed.