Recently i was looking at editorial for 992C(Nastya and wardrobe problem) and i am bit confused with the notions of expected value, even i have gone through wikipedia but still not satisfied. Please elaborate difference between **expected value** and **average**, if it is there ?? Thank you!

I think expected value here is equal to the mean because at each step the probability is becoming half (and equal for each value).

i.e. for 3 and 2 (3rd example explanation),

after 1st month, the probability of 6=50% and 5=50% (the probability is same for the values)

after 2nd month, the probability of 12=25% , 11=25%, 10=25%, 9=25% (the probability is same for the values) hence here we can take mean directly (taking 25% as common)

and after 3rd month , we just double it

At each step the probability remains same. So, its synonymous in this case. This is what I thought of ,maybe someone else will come and explain better :)

thank you sir!!

Expected Value = sigma ( (probability of occurrence of S event) * (answer if S event occur ) ) / 1

In this case, the probability is same for every possible case to happen. So expected value is just EV = ( sigma answer(i) ) / #totalCases

## totalCases are divided for probability.

** use modulus arithmetic for operations.