In a group of five people, what is the probability of finding two persons with the same month of birth?

• the probability that two of them have the same month of birth is the same as 1 - (the probability that no two of them have the same month of birth).
  
  So we will find the probability that no two of them have the same month of birth and subtract that from 1.
  
  There are 12 options for the month of birth for the first person. Since we want the next person to have a different month of birth, there are only 11 options for his month of birth. Similarly, there are only 10 options for the next person's month of birth, 9 for the next and 8 for the last.
  
  This gives 12 * 11 * 10 * 9 * 8 = 95040 ways to choose 5 people's months of birth so that no two of them are born in the same month.
  
  But, there are 12^5 = 248832 ways to choose 5 peoples months of birth (with no restrictions)
  
  So the probability that no two people share a month of birth is
  95040 / 248832 = 55 / 144
  
  And so, the probability that two people are born in the same month is 1 - 55/144
  = 89 / 144
  ≈ 61.806 %
• 13 years agoHelpfull: Yes(29) No(3)
• (12C5)/(5C2)=79.2{nCr}..!!
• 13 years agoHelpfull: Yes(3) No(4)
• there are 10 favourible combinations for same month which include pairs like
  if persons are numbered as 1,2,3,4,5 then favourible combinations are
  (1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)
  Total=10
  So probability=(10)/5C2=1/6.
  
  
• 13 years agoHelpfull: Yes(0) No(5)