# Probability that at least $2$ of a group of $4$ people were born on the same day of the week

What is the probability that at least $2$ of a group of $4$ people were born on the same day of the week?

My attempt:

Probability that at least $2$ of a group of $4$ people were born on the same day of the week=1-probability that at most $1$ of a group of $4$ people were born on the same day of the week (NONE ARE BORN ON SAME DAY).

=$1-\frac{\text{Possibility none born on same day}}{\text{No. Of total possibilites}}$ =$1-\frac{4.5.6.7}{7.7.7.7} =$0.659\$

• You need to state the assumption that the day of the week each person is born on is chosen uniformly at random and that the days were chosen independently for each person. If I go to my friend's house who I know to be a twin and his twin happens to be there, I can be sure that at least two people have the same day of the week (and in fact same birthdate) that they were born on. Or perhaps we live in a strange society where any baby born on a monday is sacrificed to the god of the moon, so you will never meet anyone born on a monday. – JMoravitz May 16 '18 at 17:45
• With those assumptions, your answer is correct. – JMoravitz May 16 '18 at 17:46
• Okay... Everything is randomly chosen – Rakesh Bhatt May 16 '18 at 17:48