2 votes 2 votes Consider that, there are 365 days in a year, what is the probability that exactly two out of ten people are born on the same day? Mathematical Logic probability engineering-mathematics + – Manu Thakur asked Jan 8, 2018 Manu Thakur 502 views answer comment Share Follow See all 10 Comments See all 10 10 Comments reply Anu007 commented Jan 8, 2018 reply Follow Share $\left (1- \left ( \frac{365\times 364.......(365-10)}{365^{10}} \right ) \right ) - \left (1- \left ( \frac{365\times 364.......(365-9)}{365^{9}} \right ) \right )$ |Atleast 2 have same day| - |atleast 3 have same day| = {2,3,4,5....} - {3,4,5..}= {2}. 0 votes 0 votes Shivam Chauhan commented Jan 8, 2018 reply Follow Share Is answer = 0.1116 0 votes 0 votes Manu Thakur commented Jan 8, 2018 reply Follow Share @anu see this question https://gateoverflow.in/3284/gate2008-it-23 and explain the second part. 0 votes 0 votes srestha commented Jan 8, 2018 reply Follow Share it can also solve by generating function right? 0 votes 0 votes Manu Thakur commented Jan 8, 2018 reply Follow Share @srestha if you see the original question, in the given solution, it is 364^(r-2) i m unable to understand this part, why is the power of 364 and not 365 0 votes 0 votes srestha commented Jan 8, 2018 reply Follow Share answer is correct there when we subtract from 1? when we are finding opposite which we are calculating=1-Probability(x) 364^(r-2) because 2 people already has same birthday So, remaining (r-2) people has to choose birth day from 364 days rt? 0 votes 0 votes sid1221 commented Jan 8, 2018 reply Follow Share its not like that particular 1 things are already selected , means if 1 person can have bday on any day . and second person have only 1 choice ...and for remaing person (365-1=364 bcoz 1 day already selected) 0 votes 0 votes Manu Thakur commented Jan 8, 2018 reply Follow Share @Srestha @sid that is ok, but that shouldn't be 365/365*1/365*364/365............ and so on? why is the sample space 364^(r-2)? 0 votes 0 votes sid1221 commented Jan 8, 2018 reply Follow Share yes its correct ... it should be rc2 /365. for remaining sample space 364^(r-2) 0 votes 0 votes srestha commented Jan 8, 2018 reply Follow Share @Manu thakur where r u getting this ? 365/365*1/365*364/365. ........ Can u tell a bit more? because I am not getting this line 0 votes 0 votes Please log in or register to add a comment.