0 votes 0 votes In a restaurant each of $n$ customer gives a hat to the hat check person. The hat check person gives the hat back to the customer in a random order. What is expected number of customer who get back their own hat? Probability algorithms probability + – srestha asked May 27, 2019 srestha 839 views answer comment Share Follow See all 11 Comments See all 11 11 Comments reply Show 8 previous comments Anuj Mishra commented May 30, 2019 reply Follow Share @Satbir , Then out of n! cases there is only 1 correct way of giving the hat back to the customers so probability = 1/n! What is it that you're calculating? Is it the probability to give everyone their correct hat? 0 votes 0 votes Satbir commented May 30, 2019 reply Follow Share Yes. 0 votes 0 votes arun yadav commented Sep 13, 2020 reply Follow Share i thought you are just considering only that case where a single customer among various customers should get their hat back. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes X : 1 1 1 1 1 .......... 1 (Till n terms) fx : 1/n 1/n 1/n 1/n 1/n 1/n (probability that he gets the correct hat back out of n hats) Now, expectation (or in other words mean)= x * $f_x$ = n* (1/n) = 1. Hirak answered May 31, 2019 Hirak comment Share Follow See all 0 reply Please log in or register to add a comment.