Answer the following questions about a family of 5 people, assuming that birthda
ID: 3206198 • Letter: A
Question
Answer the following questions about a family of 5 people, assuming that birthdays are uniformly distributed through the days of the week, month, and a year. Also assume that the year is exactly 365 days and each month is exactly 30 days.
a). What is the probability that at least two of the family members have the same birthday? What is the probability that none of them have the same birthday?
b). What is the Probability that at least two of the family members are born in the same month? and that none of them were born in the same month?
c). What is the probability that at least one of them is born on the first day of a month?
Explanation / Answer
a)probability that none of them have the same birthday =P(first one can have bthday on any day*second on rest 364*third on rest 363, 4th rest 362*fifth on rest 361) =(365*364*363*362*361)/(365)5 =0.9729
hence probability that at least two of the family members have the same birthday =1-P(none have matching bthday)
=1-0.9729=0.0271
b))probability that none of them were born on same month =P(first one can born in any 12 month, second on11, third on rest 10..) =(12*11*10*9*8)/125 =0.3819
hence Probability that at least two of the family members are born in the same month =1-0.3819=0.618
c)as there are 12 days out of 365 days.for first day of month
probability that none of them were born on 1st day of month =(1-12/365)5=0.8461
hence Probability that at least one of them were born on 1st day of month =1-0.8461=0.1539