Determine the probability that at least 2 people in a room o

Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions: Compute the probability that 10 people have different birthdays. The complement of \"10 people have different birthdays\" is \"at least 2 share a birthday\". Use this information to compute the probability that at least 2 people out of 10 share the same birthday. The probability that 10 people have different birthdays is . (Round to four decimal places as needed.)

Solution

PROBABILITY OF HAVING SAME BDAY = 1/365

PROBABILITY OF HAVING DIFFERENT BDAY = 364/365

A) NOW THE PROBABILITY THAT ALL 10 HAVE DIFFERENT BDAY = (364/365)^10 = 0.972

B) PROBABILITY THAT AT LEAST 2 HAVE SAME BDAY = 1 - P(NO SAME BDAY) ( AS ONLY 0 WILL BE COUNTED BACUASE TO SHARE AT LEAS 2 PEOPLE ARE REQUIRED)

PROBABILITY = 1 - 0.972 = 0.228