Need help in EXPXOR | May Cook-Off

Hey Everyone,
I have been trying to solve this problem from https://www.codechef.com/COOK106B/problems/EXPXOR but I am not able to understand the motto of the problem.
Help would be appreciated.

well if you don’t understand the motto of the problem you can refer the editorial and just read the problem description and don"t read the solution

However, Here is mine explanation

the question is asking you to compute the total beauty of the paintings you select in order to maximize the beauty of the exhibition that is you have to use only those paintings in xor calculation which can maximize the xor value i.e. the total beauty of the exhibition

for instance suppose that there are 5 paintings such as

   painting                  beauty               probability
   
   paint_1                     b1                     p1      
   paint_2                     b2                     p2
   paint_3                     b3                     p3
   paint_4                     b4                     p4
   paint_5                     b5                     p5

and suppose you opt paint_1 , paint_3, and paint_4 then
total beauty = b1p1 + b3p3 + b4*p4
now print this total beauty to 6 digits after the decimal and this is your required answer.

Remember that every painting you select is probably selected , not all are selected so calculate the sum with the probability i.e. calculate the total probability .

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@dragon_knight1

Example case 1: The first painting must be displayed at the exhibition, the second one must be excluded. If the third painting is displayed (with probability 0.50.5), the beauty is 5βŠ•2=75βŠ•2=7; if it is excluded (with probability 0.50.5), the beauty is 55. The expected beauty is 0.5β‹…5+0.5β‹…7=60.5β‹…5+0.5β‹…7=6.

this is the example given in the problem, I don’t understand the part 0.5β‹…5+0.5β‹…7=60.5β‹…5+0.5β‹…7=6 why 5 and 7 (which are xor ) is getting multiplied with 0.5.

sorry , shivank i just made a little mistake in my above explanation which is actually big:stuck_out_tongue_closed_eyes::stuck_out_tongue_closed_eyes:

see its just asking the total beauty

now if you know that a painting you are selecting is with beauty β€œB” and probability β€œP” then you know there still chances that the painting may not be selected which is equal to β€œ1-P” by the law of probability hence you need to multiply the beauty with the probability in order to get the total beauty. i.e β€œP*B”. its just a little math you have to consider

read the total probability rule or check this link for the same however i recommend NCERT
TOTAL PROBABILITY RULE.

i have corrected the above explanation

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