SOLUTION: assume there are 365 days in a year, from a group of 4 random people a) what is the total number of combination for their birthday b)what is the total number of combination for t

Question 1208079: assume there are 365 days in a year, from a group of 4 random people
a) what is the total number of combination for their birthday
b)what is the total number of combination for their birthday if no birthday is shared by any two people.
c)what is the probability that no birthday is shared by any two people
d)what is the probability that there is at least a shared birthday in the group.
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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assume there are 365 days in a year, from a group of 4 random people
a) what is the total number of combination for their birthday
b)what is the total number of combination for their birthday if no birthday is shared by any two people.
c)what is the probability that no birthday is shared by any two people
d)what is the probability that there is at least a shared birthday in the group.
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(a)  In a random sample of 4 people, 

        - any of the 365 days can be a birthday for the 1st person;
        - any of the 365 days can be a birthday for the 2nd person;
        - any of the 365 days can be a birthday for the 3rd person;
        - any of the 365 days can be a birthday for the 4th person.

     So, the total number of all possible different combinations for their birthdays is  .



(b)  If no birthday is shared by any two people, then the number of all possible different 
     combinations for their birthdays is  365*364*363*362.

     (365 possibilities for the 1st person; 364 for the 2nd person and so on . . . )



(c)  Using the formulas from (a) and (b), you can deduce the answer for (c)

         P(c) =  =  = 0.9836 (rounded).


(d)  The probability in (d) is the COMPLEMENT to that in (c)

         P(d) = 1 - P(c) = 1 -  = 1 - 0.9836 = 0.0164  (rounded).

Solved - all questions are answered, with explanations.

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