- Ankita and Nagma re two friends. They were both born in 1990. What is the probability that they have (1) same birth day
(2)different birth days?
here's the solution
Let Ankita be A, let Nagma be B, let the year be a normal year (365 days)
Possible birthdays : (1-1, 1-1) , (1-1, 1-2),...... (1-1, 31-12), (1-2, 1-1),.. .........................., (31-12, 31-12)
so the above total adds up to 365 * 365 = 133225
the no. of outcome when the birthday will be same is 365
so P (having same birthday ) = 365/ 133225 = 1/365 ans.(i)
and P (having different birthday) = (133225-365) / 133225 = 364/365 ans (ii)
Hope this helps!
ankita may have any one of the 365 days of the year as her birthday . similarly nagma may have any one of 365 days of the year as her birthday
total no. of ways in which ankita and nagma may have their birthday=365*365
number of ways in which ankita and nagma will have same birthday= 365/365*365=1/365
for different birtday= 1-both have same birthday = 1-1/365 = 364/365
hope it help